IC-NRLF 


B    M    OEb    llfi 


Q   D 

65 

M7 

1913 

CHEM 


UCTION  TABLES 

MOORE 


THE  usrjfet 

^ 

UtKlLlV 

LIBRARY 

vumsmcx 
JAMOMHA 


f\I 


LOGARITHMIC 
REDUCTION  TABLES 


FOR  STUDENTS  OF 
ANALYTICAL  CHEMISTRY 


BY 
CHAKLES  J.  MOORE,  Pn.D.  (VIRGINIA) 

AUSTIN   TEACHING   FELLOW   IN    .MA  ANrKD  ANALYTICAL  CHEMISTRY 
IN   HARVARD  UNIVERSITY 


GINN  AND  COMPANY 

BOSTON  •  NEW  YORK  •  CHICAGO  •  LONDON 


COPYRIGHT,  1913,  BY 
CHARLES  J.  MOORE 


ALL  EIGHTS  RESERVED 

913.7 


GINN  AND  COMPANY  •  PRO- 
PRIETORS •  BOSTON  •  U.S.A. 


M7 


TO 

THE  MEMORY  OF 

MY  DEVOTED  MOTHER 

THIS  LITTLE  VOLUME 

IS  DEDICATED 


PREFACE 

These  tables  are  intended  primarily  for  students  of  analytical  chemistry. 
My  aim  has  been  to  produce  a  book  adapted  to  the  needs  of  the  beginner, 
and,  at  the  same  time,  to  arrange  the  material  in  such  a  way  that  it  may  be 
conveniently  used  by  advanced  students  and  chemists. 

In  discussing  logarithms  I  realize  I  have  encroached  on  foreign  territory, 
but,  in  my  experience  as  a  teacher,  I  have  known  many  students  who  were 
unfamiliar  with  the  use  of  logarithms,  and  who  were  unwilling  to  acquaint 
themselves  with  the  subject  unless  it  be  presented  as  a  part  of  their  present 
work.  The  subject  ie  important  for  any  one  to  know  who  has  many  arith- 
metical computations  to  make,  and  I  hope  that  a  sufficient  number  will  profit 
by  the  explanations  to  justify  me  in  including  them.  , 

The  tables  contain  the  most  recent  trustworthy  values  to  be  found  in  the 
literature.  These  values  and  their  logarithms  have  been  checked  three  times 
in  order  to  eliminate  possible  errors. 

I  have  used  freely  Landolt-Bornstein's  Physikalisch-chemische  Tabellen, 
Ostwald-Luther's  Physiko-chemische  Messungen,  and  many  original  articles. 

C.  J.  MOORE 
CAMBRIDGE,  MASSACHUSETTS 


CONTENTS 


TABLE  PAGE 

I.   ATOMIC  WEIGHTS  OF  THE  ELEMENTS  AND  THEIR  LOGARITHMS       .       3 
II.   MULTIPLES  OF  THE  ATOMIC  WEIGHTS  OF  COMMON  ELEMENTS  AND 

TIIKIK  LOGARITHMS 5 

III.  MOLECULAR  WEIGHTS   OF  COMMON  COMPOUNDS  AND  THEIR  LOGA- 

RITHMS         7 

IV.  MULTIPLES  OF  THE  MOLECULAR  WEIGHTS  OF  SOME  COMMON  COM- 

POUNDS   AND    OF    THE    WEIGHTS    OF    A    FEW    RADICALS    TOGETHER 

WITH  THEIR  LOGARITHMS 10 

V.   REDUCTION  OF   COMPOUNDS  FOUND  TO  CONSTITUENTS  SOUGHT  BY 

MULTIPLICATION           11 

VI.   REDUCTION  OF  BAROMETRIC  READINGS  TO  0° '.     .     .  16 

VII.    GEOGRAPHICAL    LATITUDE,   ELEVATION,    AND    GRAVITY    OF    SOME 

IMPORTANT  CITIES        17 

VIII.    REDUCTION  OF  BAROMETRIC  READINGS  TO  NORMAL  GRAVITY   .     .  18 

IX.   CAPILLARY  DEPRESSION  OF  MERCURY       19 

X.   TENSION  OF  AQUEOUS  VAPOR 20 

XL    REDUCTION  OF  WATER  PRESSURE  TO  MERCURY  PRESSURE    .     .     .21 

XII.    REDUCTION  OF  THE  VOLUME  OF  GASES  TO  NORMAL  PRESSURE      .  22 

XIII.  REDUCTION  OF  THE  VOLUME  OF  GASES  TO  0°C 25 

XIV.  REDUCTION  OF  THE  VOLUME  OF  GASES  SATURATED  WITH  AQUEOUS 

VAPOR  TO  0°,  NORMAL  PRESSURE,  AND  DRY 28 

XV.    OBSERVED  DENSITY  AND  THE  WEIGHT  OF  A  LITER  OF  SOME  COM- 
MON GASES 30 

XVI.    DENSITY  OF   DRY  ATMOSPHERIC   AIR   AT  760   MM.  PRESSURE  AND 

TEMPERATURES  RANGING  FROM  0°  TO  35° 31 

XVII.   APPARENT  WEIGHT  OF  A  CUBIC  CENTIMETER  OF  WATER  AND  THE 
VOLUME  OF  AN  APPARENT  GRAM  OF  WATER  AT  TEMPERATURES 

FROM  10°  TO  25° 34 

XVIII.   SPECIFIC  VOLUME  OF  WATER  AT  TEMPERATURES  FROM  0°  TO  35°     .     35 
XIX.   DENSITY  OF  WATER  AT  TEMPERATURES  FROM  0°  TO  35°       ...     36 
XX.   THE  PROPORTION  BY  WEIGHT  OF  ABSOLUTE  ALCOHOL  IN  100  PARTS 
OF  SPIRITS  OF  DIFFERENT  SPECIFIC  GRAVITIES,  AND  THE  PROPOR- 
TION BY  VOLUME  OF  ABSOLUTE  ALCOHOL  IN  100  VOLUMES  OF 

SPIRITS  OF  DIFFERENT  SPECIFIC  GRAVITIES 37 

•  vii 


viii  CONTENTS 

TABLE  PAGE 

XXL   SPECIFIC  GRAVITY  OF  SOLUTIONS  OF  AMMONIUM  HYDROXIDE    .  38 

XXII.    SPECIFIC  GRAVITY  OF  SOLUTIONS  OF  HYDROCHLORIC  ACID  .     .  38 

XXIII.  CONSTANT  BOILING  SOLUTION  OF  HYDROCHLORIC  ACID      ...  39 

XXIV.  SPECIFIC  GRAVITY  OF  NITRIC  ACID 40 

XXV.   SPECIFIC  GRAVITY  OF  SULPHURIC  ACID 41 

XXVI  A~}     CORRECTIONS  FOR  THE  EXPOSED  THREAD  OF  MERCURY  THER- 

XXVI B)         MOMETERS .   43, 44 

XXVII.   FIXED  POINTS  OF  THE  THERMOMETRIC  SCALE 44 

XXVIII.   CORRECTIONS  FOR  Loss  OF  WEIGHT  IN  AIR 45 

XXIX.   TABLE  OF  LOGARITHMS  TO  Six  PLACES  OF  DECIMALS  ....  46 

EXPLANATIONS  OF  THE   PRECEDING  TABLES 65 

DISCUSSION    OF    LOGARITHMS    AND   DIRECTIONS    FOR  USING    THE   TABLE 

OF  LOGARITHMS     .  73 


LOGARITHMIC  REDUCTION  TABLES 


TABLE  I 


THE  ATOMIC  WEIGHTS  OF  THE  ELEMENTS  AND  THEIR  LOGARITHMS 


Symbol 

Atomic 
weight 

Logarithm 

Aluminum 

Al 

27.1 

.432  969 

Antimony 

Sb 

119.86 

.078  674 

Argon 

A 

39.9 

.600  973 

Arsenic 

As 

74.95 

.874  772 

I  Jarium 

Ba 

137.36 

.137860 

Bismuth 

Bi 

208.0 

.318063 

Boron 

B 

11.0 

.041  393 

Bromine 

Br 

79.909 

.902  596 

Cadmium 

Cd 

112.41 

.050  805 

Caesium 

Cs 

132.80 

.123  198 

Calcium 

Ca 

40.07 

.602  819 

Carbon 

C 

12.00 

.079  181 

Cerium 

Ce 

140.24 

.146  872 

Chlorine 

Cl 

35.454 

.549  665 

Chromium 

Cr 

52.00 

.716003 

Cobalt 

Co 

58.96 

.770  557 

Columbium 

Cb 

93.5 

.970  812 

Copper 

Cu 

63.57 

.803  252 

Dysprosium 

Py 

162.5 

.210853 

Erbium 

Er 

167.4 

.223  755 

Europium 

Eu 

152.0 

.181  844 

Fluorine 

F 

19.0 

.278  754 

Gadolium 

Gd 

157.3 

.196  729 

Gallium 

Ga 

!69.9 

.844  477 

Germanium 

Ge 

72.5 

.860338 

Glucinum 

Gl 

9.1 

.959  041 

Gold 

Au 

197.2 

.294  907 

Helium 

He 

4.0 

.602060 

Hydrogen 

H 

1.0078 

.003  375 

Indium 

In 

114.8 

.059942 

Iodine 

I 

126.91 

.103  496 

Iridium 

Ir 

193.1 

.285  782 

Iron 

Fe 

55.83 

.746  868 

Krypton 

Kr 

81.8 

.912  753 

Lanthanum 

La 

139.0 

.143  015 

Lead 

Pb 

207.07 

.316117 

Lithium 

Li 

6.939 

.841  297 

Lutecium 

Lu 

174.0 

.240  549 

Magnesium 

Mg 

24.32 

.385  964 

Manganese 

Mn 

54.92 

.739  731 

«a. 


TABLE  I   (CONTINUED) 


Symbol 

Atomic 
weight 

Logarithm 

Mercury 
Molybdenum 
Neodymium 
Neon 

Hg 
Mo 
Nd 

Ne 

200.61 
96.0 
144.26 
20.0 

.302  353 
.982  271 
.159  146 
.301  030 

Nickel 

Ni 

58.67 

.768  416 

Nitrogen 
Osmium 

N 
Os 

14.01 
190.9 

.146438 
.280  806 

Oxygen 
Palladium 

0 
Pd 

16.000 
106.7 

.204  120 
.028  164 

Phosphorus 
Platinum 

P 
Pt 

31.03 
195.0 

.491  782 
.290035 

Potassium 

K 

39.091 

.592  077 

Praseodymium 
Kadium 

Pr 
Ra 

140.6 
225.95 

.147  985 
.354012 

Rhodium 

Rh 

102.9 

.002415 

Rubidium 

Rb 

85.44 

.931661 

Ruthenium 

Ru 

101.7 

.007  321 

Samarium 

Sa 

150.4 

.177248 

Scandium 

Sc 

44.1 

.644  439 

Selenium 

Se 

79.2 

.898  725 

Silicon 

Si 

28.3 

.451  786 

Silver 
Sodium 

Ag 

Na 

107.87 
22.993 

.032  901 
.361  595 

Strontium 

Sr 

87.613 

.942  569 

Sulphur 
Tantalum 

S 
Ta 

32.07 
181.5 

.506  099 

.258877 

Tellurium 

Te 

127.5 

.105  510 

Terbium 

Tb 

159.2 

.201  943 

Thallium 

Tl 

204.0 

.309  630 

Thorium 

Th 

232.40 

.366  236 

Thulium 

Tu 

168.5 

.226  600 

Tin 

Sn- 

119.0 

.075  547 

Titanium 

Ti 

48.1 

.682  145 

Tungsten 
Uranium 

w 

u 

184.0 
238.40 

.264  818 
.377  306 

Vanadium 

V 

51.2 

.709  270 

Xenon 

Xe 

128.0 

.107210 

Ytterbium 

Yb 

172.0 

.235  528 

Yttrium 

Y 

89.0 

.949  390 

Zinc 

Zn 

65.36 

.815312 

Zirconium 

Zr 

90.6 

.957  128 

TABLE  II 


SECOND  TO  SEVENTH  MULTIPLES  OF  THE  ATOMIC  WEIGHTS  OF 
COMMON  ELEMENTS  AND  THEIR  LOGARITHMS 


2 

log 

3 

log 

4 

log 

Aluminum 

54.2 

733  999 

81.3 

910090 

108.4 

035  029 

Antimony 

239.72 

379704 

359.58 

555  796 

479.44 

680  734 

Arsenic 

149.90 

175  802 

224.85 

351  892 

299.80 

476  832 

Barium 

274.72 

438  890 

412.08 

614  982 

549.44 

739  920 

Bismuth 

416.0 

619093 

624.0 

795  185 

832.0 

920  123 

Boron 

22.0 

342  423 

33.0 

518514 

44.0 

643  453 

Bromine 

159.818 

203  626 

239.727 

379  717 

319.636 

504656 

Cadmium 

224.82 

351  835 

337.23 

527  927 

449.64 

652  865 

Calcium 

80.14 

903  849 

120.21 

079  941 

160.28 

204879 

Carbon 

24.00 

380211 

36.00 

556  303 

48.00 

681  241 

Chlorine 

70.908 

850  695 

106.362 

026  787 

141.816 

151  725 

Chromium 

104.00  . 

017033 

156.00 

193  125 

208.00 

318063 

Cobalt 

117.92 

071  588 

176.88 

247  679 

235.84 

372618 

Copper 

127.14 

104  282 

190.71 

280374 

254.28 

405  312 

Fluorine 

38.0 

579784 

57.0 

755  875 

76.0 

880  814 

Gold 

394.4 

595  937 

591.6 

772  028 

788.8 

896  967 

Hydrogen 

2.0156 

304  405 

3.0234 

480  496 

4.0312 

605  434 

Iodine 

253.82 

404  526 

380.73 

580617 

507.64 

705  556 

Iron 

111.66 

047  898 

167.49 

223  989 

223.32 

348  928 

Lead 

414.14 

617  147 

621.21 

793  238 

828.28 

918177 

Lithium 

13.878 

142  327 

20.817 

318418 

27.756 

443  357 

Magnesium 

48.64 

686994 

72.96 

863  085 

97.28 

988024 

Manganese 

109.84 

040  760 

164.76 

216852 

219.68 

341  790 

Mercury 

•  401.22 

603  383 

601.83 

779  474 

802.44 

904413 

Molybdenum 

192.0 

283  301 

288.0 

459  392 

384.0 

584331 

Nickel 

117.34 

069  446 

176.01 

245  537 

234.68 

370476 

Nitrogen 

28.02 

447  468 

42.03 

623  559 

56.04 

748498 

Oxygen 

32.000 

505  150 

48.000 

681  241 

64.000 

806  181 

Phosphorus 

62.06 

792  812 

93.09 

968903 

124.12 

093  842 

Platinum 

390.0 

591  065 

585.0 

767  156 

780.0 

892  095 

Potassium 

78.182 

893  107 

117.273 

069  198 

156.364 

194  137 

Silicon 

56.6 

752  816 

84.9 

928  908 

113.2 

053  846 

Silver 

215.74 

333  930 

323.61 

510022 

431.48 

634  961 

Sodium 

45.986 

662  626 

68.979 

838717 

91.972 

963  655 

Strontium 

175.226 

243  598 

262.839 

419  690 

350.452 

544  628 

Sulphur 

64.14 

807  129 

96.21 

983  220 

128.28 

108  159 

Tin 

238.0 

376577 

357.0 

552  668 

476.0 

677  607 

Titanium 

96.2 

983  175 

144.3 

159  266 

192.4 

284  205 

Tungsten 

368.0 

565  848 

552.0 

741  939 

736.0 

866  878 

Uranium 

476.8 

678  336 

715.2 

854  428 

953.6 

979  366 

Zinc 

130.72 

116343 

19608 

292  433 

261.44 

417372 

TABLE  II  (COXTIXUED) 


5 

log 

6 

log 

7 

log 

Aluminum 

135.5 

131  939 

162.6 

211  121 

189.7 

278  067 

Antimony 

599.30 

777  644 

719.16 

856  826 

839.02 

923  772 

Arsenic 

374.75 

573  742 

449.70 

652  923 

524.65 

719  869 

Barium 

686.80 

836  830 

824.16 

916012 

961.52 

982  958 

Bismuth 

1040.0 

017033 

-1248.0 

096  215 

1456.0 

163  161 

Boron 

55.0 

740  363 

66.0 

819  544 

77.0 

886491 

Bromine 

399.545 

601566 

479.454 

680  747 

559.363 

747  694 

Cadmium 

562.05 

749  775 

674.46 

828  956 

786.87 

895  903 

Calcium 

200.35 

301  789 

240.42 

380971 

280.49 

447  917 

Carbon 

60.00 

778151 

72.00 

857333 

84.00 

924  279 

Chlorine 

177.270 

248  635 

212.724 

327816 

248.178 

394  763 

Chromium 

260.00 

414973 

312.00 

494  155 

364.00 

561  101 

Cobalt 

294.80 

469  528 

353.76 

548  709 

412.72 

615  656 

Copper 

317.85 

502  222 

381.42 

581  404 

444.99 

648  350 

Fluorine 

95.0 

977  724 

114.0 

056  905 

133.0 

123  852 

Gold 

986.0 

993  877 

1183.2 

073  058 

1380.4 

140  005 

Hydrogen 

5.0390 

702  344 

6.0468 

781  526 

7.0546 

848  472 

Iodine 

634.55 

802  466 

761.46 

881  647 

888.37 

948  594 

Iron 

279.15 

445  838 

334.98 

525  019 

390.81 

591  966 

Lead 

1035.35 

015  087 

1242.42 

094  269 

1449.49 

161  215 

Lithium 

34.695 

540  267 

41.634 

619  448 

48.573 

686  395 

Magnesium 

]  21.60 

084  934 

145.92 

164  115 

170.24 

231  062 

Manganese 

274.60 

438  701 

329.52 

517881 

384.44 

584  828 

Mercury 

1003.05 

001323 

1203.66 

080  504 

1404.27 

147451 

Molybdenum 

480.0 

681  241 

576.0 

760  422 

672.0 

827369  • 

Nickel 

293.35 

467  386 

352.02 

546  567 

410.69 

613514 

Nitrogen 

70.05 

845  408 

84.06 

924589 

98.07 

991  536 

Oxygen 

80.000 

903090 

96.000 

982  271 

112.000 

049  218 

Phosphorus 

155.15 

190  752 

186.18 

269  933 

217.21 

336  880 

Platinum 

975.0 

989  005 

1170.0 

068  186 

1365.0 

135  133 

Potassium 

195.455 

291  047 

234.546 

370  228 

273.637 

437  175 

Silicon 

141.5 

150  756 

169.8 

229  938 

198.1 

296  884 

Silver 

539.35 

731  870 

647.22 

811052 

755.09 

877  998 

Sodium 

114.965 

060  566 

137.958 

139  747 

160.951 

206  694 

Strontium 

438.065 

641  538 

525.678 

720  720 

613.291 

787  667 

Sulphur 

160.35 

205  069 

192.42 

284-250 

224.49 

351  197 

Tin 

595.0 

774517 

714.0 

853  698 

833.0 

920  645 

Titanium 

240.5 

381  115 

288.6 

460296 

336.7 

527  243 

Tungsten 

920.0 

963  788 

1104.0 

042  969 

1288.0 

109  916 

Uranium 

1192.0 

076  276 

1430.4 

155457 

1668.8 

222  404 

Zinc 

326.80 

514282 

392.16 

593  463 

457.52 

660  410 

TABLE  III 


MOLECULAR  WEIGHTS  OF  COMMON  COMPOUNDS  AND  THEIR  LOGARITHMS 


Mol.wt. 

log 

Mol.  wt. 

log 

AgBr 

187.779 

273  647 

Cr03 

100.00 

000  000 

AgCN 

133.88 

126  716 

Cr04 

116.00 

064  458 

AgCl 

143.324 

156319 

Cu20 

143.14 

155  761 

Agl 

234.78 

370661 

CuO 

79.57 

900  749 

As"NO 

169.88 

230  142 

Cu2S 

159.21 

201  970 

A120,  3 

102.2 

009451 

CuS 

95.64 

980  640 

A12(S04)3.18H20 

666.69 

823  924 

CuS04 

159.64 

203  142 

AsA 

197.90 

296446 

CuS04-5H20 

249.72 

397  453 

AsO 

229.90 

361  539 

FeC03 

115.83 

063  821 

•2     5 

As03 

122.95 

089  729 

FeCl2.4H20 

198.80 

298416 

As04 

138.95 

142  859 

FeCL 

162.19 

210  024 

As2S3 

246.11 

391  130 

FeO 

71.83 

856  306 

As/6 

310.25 

491  712 

Fe20_ 

159.66 

203  196 

BA1 

70.0 

845  098 

FeP04 

150.86 

178574 

BaC03 

197.36 

295  259 

FeS 

87.90 

943  939 

BaCL 

208.27 

318627 

FeS04 

151.90 

181  558 

BaCl2-2H20 

244.30 

387  923 

FeS04-7H20 

278.01 

444060 

BaCr04 

253.36 

403  738 

HBO, 

62.0 

792  392 

Ba(N03)2 

261.38 

417273 

HBr 

80.917 

908  040 

BaO 

153.36 

185  712 

HCH02 

46.02 

662947 

Ba(OH)2  •  8  H20 

315.50 

498999 

HC2H302 

60.03 

778  368 

BaS04 

233.43 

368  157 

H,C,04 

90.02 

954  339 

BaSiF6 

279.66 

446630 

H2C204-2H20 

126.05 

100543 

BjA 

464.0 

666518 

H2C4H406 

150.05 

176236 

BLS 

512.2 

709  440 

H3C6H50T.H20 

210.08 

322  323 

cd, 

44.00 

643  453 

HC1 

36.462 

561  840 

C.70 

88.00 

944  483 

HC104 

100.462 

002  002 

3 

60.00 

778151 

HsCrA 

218.02 

338  496 

CaC08 

100.07 

000304 

H2004 

118.02 

071  956 

CaCl2 

110.98 

045245 

HF 

20.0 

301  030 

CaCL.6HaO 

219.07 

340  583 

HI 

127.918 

106932 

CaO 

56.07 

748731 

HNO 

63.02 

799478 

CaS04 

136.14 

133  986 

H20  3 

18.0156 

255649 

CaS04  •  2  H20 

172.17 

235  958 

H00 

34.0156 

531  678 

CdO 

128.41 

108599 

H  PO 

98.05 

991  448 

CdS 

144.48 

159  808 

H2Pt(Jl6 

409.7 

612  466 

CdS04 

208.48 

319064 

H2S 

34.09 

532  627 

CoO 

74.96 

874  830 

H2S03 

82.09 

914290 

CoS04 

155.03 

190416 

H2S04 

98.09 

991  625 

CoS04  •  7  H20 

281.14 

448  923 

Hg2Cl2 

472.13 

674  062 

CrA 

152.00 

181  844 

HgCl2 

271.52 

433  802 

TABLE  III  (CONTINUED) 


Mol.wt. 

log 

Mol.wt. 

log 

KA1(S04)2-12H20 
KA1SLO, 
KBr 

474.5 
279.1 
119.000 

676  236 

445  760 
075  547 

NH4C1 

(NH4)2Fe(S04)2-6HO 
NH4Fe(S04)2.12H20 

53.50 
392.14 
482.19 

728  354 
593  441 
683  218 

KCN 

65.10 

813  581 

NHOH 

35.05 

544  688 

138.13 
74.545 

140  288 

872  419 

(NH4)3P04(Mo03)12 
(NH4)2PtCl6 

1877.2 
443.8 

273511 
647187 

KC103 

122.545 

088  296 

(NH4)2S04 

132.15 

121067 

KC104 

138.545 

141  591 

NaAlSi308 

263.0 

419  956 

K  Co(NO  ) 

452.29 

655417 

Na  B  0 

202.0 

305  351 

K2Cr04 

194.18 

288  205 

Na2BX-10H20 

382.1 

582  177 

K2Cr2O. 

294.18 

468  613 

NaBr    7 

102.902 

012  424 

KCr(S04)2-12H20 

K3Fe(CN)6 

499.42 
329.15 

698466 
517394 

NaC2H302.3H20 

Na2C03 

136.06 
105.99 

133  730 
025  265 

K4Fe(CN)6 

368.24 

566131 

Na2C03-10H20 

286.14 

456579 

KI 

166.001 

220111 

NaCl 

58.447 

766  762 

KI03 

214.001 

330416 

Na2O207  •  2  H20 

298.02 

474  245 

KMn04 

158.01 

198  685 

NaHCO 

84.00 

924  279 

KNO 

85.10 

929  930 

Na9HP04.12H20 

358.24 

554  174 

KN03 

101.10 

004751 

NaHSO4 

120.07 

079  435 

KNaC4H40  6-4H20 

282.18 

450  526 

NaNO 

69.00 

838  849 

K20 

94.182 

973  968 

NaN03 

85.00 

929  419 

KOH 

56.099 

748  955 

3 

61.986 

792  294 

K2PtCl6 
K2S04 

485.9 
174.25 

686  547 
241  173 

Na202 
NaOH 

77.986 
40.00 

892017 
602060 

MgC03 

84.32 

925  931 

Na2S20  -5H20 

248.20 

394  802 

MgCl2.6H20 

203.32 

308  180 

Na2S03.7H20 

252.17 

401  693 

MgO 

40.32 

605  521 

Na2S04 

142.06 

152472 

Mg  P  0 

222.70 

347  720 

Na2S04.10H20 

322.21 

508  139 

Mgsd4  7 

120.39 

080590 

u  2          4                    2 

74.67 

873  146 

MgS04-7H20 

246.50 

391  817 

NiS04 

154.74 

189  603 

MnC03 

114.92 

060  396 

NiS04-7H20 

280.85 

448  474 

MnO 

70.92 

850  769 

N03 

62.01 

792  462 

Mn203 

157.84 

198  217 

PCL 

137.39 

137955 

Mn304 

228.76 

359  380 

PBr3 

270.76 

432  585 

Mn02 

86.92 

939  120 

P2°8 

110.06 

041630 

Mn^°7 

MnS 

283.90 
86.99 

453  165 
939  469 

2      o 

?K 

142.06 
95.03 

152472 
977  861 

MnS04 

150.99 

178948 

PbC03 

267.07 

426  625 

MnS04-4H20 

223.05 

348  402 

PbCl2 

277.98 

444014 

NH 

17.03 

231215 

PbCr04 

323.07 

509  297 

NH 

18.04 

256  237 

Pb(N03)2 

331.09 

519946 

(NH4)2C204.H20 

142.10 

152  594 

PbO 

223.07 

348441 

TABLE  III  (CONTINUED) 


Mol.wt. 

log 

Mol.wt. 

log 

PbS 

239.14 

378652 

SnO 

135.0 

130334 

PbSO, 

303.14 

481  643 

Sn02 

151.0 

178977 

PtCl. 

336.8 

527372 

SrCO 

147.61 

169  116 

S02 

64.07 

806655 

Sr(NO) 

211.63 

325  577 

S03 

80.07 

903  470 

SrO 

103.613 

015  414 

S04 

96.07 

982  588 

Sr(OH)  2-8H20 

265.754 

424  480 

Si02 

60.3 

780317 

SrS04 

183.68 

264  062 

Si03 

76.3 

882  525 

ZnCd 

125.36 

098  159 

SiO. 

92.3 

965  202 

ZnO 

81.36 

910411 

SnCl2 

189.9 

278  525 

ZnS 

97.43 

988693 

SnCl2-2H,0 

225.9 

353916 

ZnS04  •  7  H20 

287.54 

458  698 

SnCl4 

260.8 

416  308 

10 


TABLE  IV 


SECOND  TO  FIFTH  MULTIPLES  OF  THE  MOLECULAR  WEIGHTS  OF  SOME 

COMMON   COMPOUNDS  AND  OF  THE  WEIGHTS  OF  A  FEW   RADICALS 

TOGETHER  WITH  THEIR  LOGARITHMS 


2 

log 

3 

log 

4 

log 

5 

log 

AgBr 

375.558 

574677 

563.337 

750  768 

751.116 

875  707 

938.895 

972617 

AgCl 

286.648 

457349 

429.972 

633  440 

573.296 

758379 

716.620 

855  289 

Agl 

469.56 

671  691 

704.34 

847  782 

939.12 

922  721 

1173.90 

069631 

A10 

204.4 

310481 

306.6 

486572 

408.8 

611511 

511.0 

708421 

Ba(OH)2 

342.75 

534977 

514.13 

711073 

685.50 

836007 

856.88 

932920 

Ba(OH)2.8H20 

631.00 

800029 

946.50 

976  121 

1262.00 

101059 

1577.5 

197  969 

C02 

88.00 

944483 

132.00 

120574 

176.00 

245  513 

220.00 

342  423 

CO 

120.00 

079181 

180.00 

255  273 

240.00 

380211 

300.00 

477121 

CaO 

112.14 

049  761 

168.21 

225  852 

224.28 

350  791 

280.35 

447  701 

Cr  0 

304.00 

482  874 

456.00 

658965 

608.00 

783904 

760.00 

880814 

Cub3 

159.14 

201  779 

238.71 

377871 

318.28 

502  809 

397.85 

599  719 

FeO 

143.64 

157275 

215.46 

333  367 

287.28 

458305 

359.10 

555215 

Fe203 

319.28 

504172 

478.92 

680263 

638.56 

805  202 

798.20 

902112 

HCHO 

92.03 

963  929 

138.05 

140036 

184.06 

264959 

230.10 

361917 

HC  H  0 

120.06 

079398 

180.09 

255  490 

240.13 

380446 

300.15 

477338 

H  C  0 

180.03 

255  345 

270.05 

431  444 

360.06 

556375 

450.10 

653  309 

H2C204-2H20 

252.09 

401556 

378.14 

577653 

504.19 

702  594 

630.25 

799513 

H  C  H  0 

300.09 

477251 

450.14 

653348 

600.19 

778  289 

750.25 

875  206 

H3C6H507-H20 

420.16 

623415 

630.23 

799499 

840.31 

924  440 

1050.2 

021  293 

HC1 

72.924 

862  870 

109.385 

038958 

145.847 

163  898 

182.31 

260810 

HNO 

126.04 

100  508 

189.05 

276577 

252.07 

401  521 

315.10 

498  448 

H20 

36.0312 

556700 

54.0468 

732  828 

72.0614 

857  724 

90.0780 

954619 

H2S04 

196.17 

292  633 

294.26 

468  731 

392.34 

593  663 

490.45 

690  595 

K20 

188.364 

274998 

282.546 

451089 

376.728 

576028 

470.910 

672938 

KOH 

112.198 

049985 

168.296 

226074 

224.395 

351013 

280.49 

447925 

MgO 

80.64 

906551 

120.96 

082  642 

161.28 

207  581 

201.60 

304491 

NH3 

34.07 

532372 

51.10 

708421 

68.13 

833  338 

85.15 

930  185 

NH4 

36.08 

557267 

54.12 

733  358 

72.16 

858297 

92.30 

965  207 

NH4OH 

70.1 

845  718 

105.15 

021  809 

140.20 

146  748 

175.25 

243  658 

N03 

124.02 

093  492 

186.03 

269583 

248.04 

394  522 

310.05 

491  432 

Na2C08 

211.97 

326274 

317.96 

502372 

423.94 

627304 

529.95 

724  235 

NaOH 

80.002 

903100 

120.002 

079  188 

160.003 

204  128 

200.00 

301  030 

OH 

34.0156 

531  678 

51.0234 

707  769 

68.0312 

832  708 

85.039 

929618 

po4 

190.06 

278  891 

285.09 

454982 

380.12 

579921 

475.15 

676831 

-P9O, 

284.12 

453  502 

426.18 

629  593 

568.24 

754  532 

710.30 

851442 

s625 

128.14 

107685 

192.21 

283  776 

256.28 

408715 

320.35 

505  625 

S03 

160.14 

204  500 

240.21 

380  591 

320.28 

505  530 

400.35 

602  440 

S04 

192.14 

283  618 

288.21 

459  709 

384.28 

584  648 

480.35 

681  558 

Si02 

120.6 

081  347 

180.9 

257439 

241.2 

382377 

301.5 

479  287 

Si03 

152.6 

183  555 

228.9 

359646 

305.2 

484585 

381.5 

581  495 

SiO 

184.6 

266232 

276.9 

442  323 

369.2 

567  262 

461.5  ' 

664172 

TABLE  V 


11 


REDUCTION  OF  COMPOUNDS  FOUND  TO  CONSTITUENTS  SOUGHT 
BY  MULTIPLICATION 


Sought 

Found 

Factor 

log 

Ag 

AgBr 

.57445 

759  254 

AgCl 

.75  263 

876  582 

Al 

Al  0 

.53  033 

724  548 

As 

As,o' 

.75  745 

879  356 

AsX 

.65  202 

814  263 

AsA 

.60908 

784  672 

AsS. 

.48316 

684  090 

MgNH.AsO..H,0 

Mg2As207 

.37601 
.48  270 

575  200 
683  684 

As203 

As206 

.86081 

934  907 

As2S3 

.80411 

905316 

-A-S  j^r 

.63  787 

804734 

MgNH.AsO  -H20 

.49  641 

695  844 

As205 

Mg2As207 

As2S3 

.63  728 
.93  413 

804  328 
970  409 

As03 

As2S3 

.99914 

999629 

AsO 

AsS 

1.12917 

052  759 

Ba 

BaO8 

.89  568 

952  148 

BaC03 
BaCr04 

.69  599 
.54213 

842  601 
734  103 

BaSO. 
BaSiF6 

.58  844 
.49117 

769  703 
691  230 

BaO 

BaC03 

.77  706 

890453 

BaSO, 

.65  698 

817555 

Bi 

WA 

.89  655 

952  575 

Bi2S3 

.81217 

909645 

B 

.31  428 

497  325 

KBF 

.08  723 

940  666 

Br 

AgBr 

.42  555 

628  949 

C 

CaCO. 

.27  273 
.43  969 

435  728 
643  149 

CaO 

.78473 

894  722 

MgO 

1.09  127 

037  932 

C°3 

Ca 

CO 
CaCO3 

1.36363 
.40  042 

134698 
602515 

CaO 

.71  464 

854088 

CaS04 

.29  433 

468  833 

CaC03 

CaO 

1.78473 

251  573 

CaSO. 

.73  505 

866318 

CaO 

C02 

1.27432 

105  278 

12 


TABLE  V  (CONTINUED) 


Sought 

Found 

Factor 

log 

CaO 

CaC03 

.56031 

748  427 

CaSO, 

.41  186 

614  745 

Cd 

CdO 

.87  540 

942  206 

CdS 

.77  803 

890  997 

CdSO, 

.53919 

731  741 

CdO 

CdS 

.88  877 

948  791 

CdS04 

.61  593 

789  535 

Cl 

Ag 

.32  867 

516764 

Cl 

AgCl 

.24  737 

393  346 

Co 

CoO 

.78  655 

895  727 

CoS04 

.38031 

580  141 

2CoS04-3K2S04 

.14159 

151041 

2CoK  (NO.)  -3H20 

.12300 

089  922 

CoO 

Co 

1.27137 

104273 

CoS04 

.48  352 

684  414 

2CoS04-3K2S04 

2CoS04K3(N02)6-3H20 

.18002 
.15  638 

255  314 
194  195 

Cr 

BaCr04 

.20  524 

312  265 

Cr  () 

.68421 

835  189 

PbCr04 

.16096 

206  706 

Cr  0 

BaCr04 

.29  997 

477076 

PbCr04 

.23  524 

371517 

Cr03 

BaCrO, 

.39  470 

596  262 

Cr203 

1.31  579 

119186 

PbCi04 

.30  953 

490  703 

Cr04 

BaCrO, 

.45  784 

660  710 

Cr  0 

1.52631 

183  644 

PbCrO, 

.35  905 

555  161 

Cu 

CuO 

.79  892 

902  503 

CuS 

.79857 

902312 

CuO 

Cu 

1.25  169 

097  497 

Cu2S 

.99  956 

999  809 

F 

CaF2 

.48  662 

687  189 

SiF4 

.72  866 

862  530 

Fe 

FeA" 

.69  932 

844  678 

FeS3 

.63511 

802  851 

FeO 

Fe 

1.28663 

109  455 

FeA 

.89  977 

954  133 

Fe  0 

Fe 

1.42995 

155  322 

H2 

H20 

.11  188 

048  756 

HBr 

AgBr 

.43  092 

634  393 

HC1 

AgCl 

.25  440 

405  521 

TABLE  V  (CONTINUED) 


13 


Sought 

Found 

Factor 

log 

HI 

Agl 

.54  484 

736  271 

HKO 

NH4C1 

1.17794 

071  124 

(NH4)2PtCl6 

.28  400 

453  321 

Pt 

.64  635 

810  473 

H2S04 

BaS04 
Hg.2Cl2 
HgS 

.42  021 
.84  981 
.86217 

623  468 
929  321 
935  594 

Hg20 

Hg 

1.03  988 

016  982 

HgO 

Hg 

1.07  976 

033  326 

I 

Agl 

.54  055 

732  835 

PdI2 

.70  408 

847621 

K 

KC1 

.52  439 

719658 

K2PtCl6 

.16090 

206  560 

K 

Pt 

.40  093 

603  072 

K2SO 

.44868 

651934 

KC1 

K  PtCl 

.30  683 

486  902 

Pt 

.76457 

883  414 

K20 

KC1 

.63  171 

800519 

KNO_ 

.46579 

668187 

K2PtCl6 

.19383 

287  421 

Pt 

.48  298 

683  933 

K2S04 

.54  050 

732  795 

T7"    Qf~\ 

J\-JO\J. 

BaS04 

.74648 

873  016 

Li 

Li20 

.46  449 

666975 

Li  CO 

.18  784 

273  800 

Li3P04 

.17  967 

254  483 

Li2S04 

.12622 

101  131 

Li20 

Li2C03 

.40  441 

606  825 

Li3P04 

.38  682 

587  506 

Li2S04 

.27  174 

434  156 

Mg 

MgO 

.60317 

780  443 

MgC03 

Mg2P207 
MgO 

.21  839 
2.09  127 

339  235 
320410 

Mg2P207 

.75  718 

879  199 

MgO 

Mg2P207 

.36  207 

558  792 

Mn 

MnO 

.77439 

888  962 

Mn208 

.69  590 

842  544 

Mn304 

.72  023 

857472 

Mn2P207 

.38  690 

587  596 

MnS 

.63  134 

800  262 

MnS04 

.36373 

560  783 

MnO 

MnS 

.81  527 

911  300 

14 


TABLE  V  (CONTINUED) 


Sought 

Found 

Factor 

log 

MnO 

MnS04 

.46  970 

671  821 

N 

NH 

.82  266 

915  223 

(NH4)2PtCl6 

.06  314 

800  281 

Pt 

.14  369 

157433 

NH 

N 

1.21556 

084  777 

NH4C1 

(NH4)2PtCl6 

.31  832 
.07  675 

502  861 

885  058 

Pt 

.17466 

242  210 

NH4 

NH4C1 

.33  720 

527  883 

3 

(NH4)2PtCl6 
NHC1 

.08  130 
1.15  907 

910080 
064  108 

(NH4)2PtCL 

.27  945 

446  305 

Pt 

.63600 

803  457 

Na 

_IM  ct~  V-J 

.74  187 

870331 

NaCl 

.39340 

594  833 

NaN03 

.27051 

432  176 

Na2S04 

.32371 

510153 

NaCl 

Na2S04 

.82  285 

915  320 

Na20 

NaCl 

.53  028 

724  502 

NaNO 

.36  462 

561  845 

Na  SO 

.43  634 

639  822 

Na2S04 

BaS04 

.60  858 

784  315 

Ni 

NiO 

.78572 

895  270 

NiO 

Ni 

1.27271 

104  730 

P 

P205 

.43  686 

640  340 

Mg  P  O 

.27  867 

445  092 

(NH4)^04.12Mo03 

.01  653 

218271 

P20g 

Ag3P04 

.16  967 

229  601 

(NHlP04-12MoOa 

(U02)2P207 

.63  790 
.03  784 
.19872 

804752 
577931 
298251 

P04 

Mg2P207 

.85  344 

931  171 

Pb 

(NH4)2P04-12Mo08 
PbCr04 

.05  062 
.64094 

704  350 
806  820 

PbO 

.92  827 

967  676 

Pb02 

.86  615 

937  592 

PbS 

.86  589 

937  465 

PbO 

PbSO. 
PbCr04 

.68  309 
.69047 

834474 
839  144 

PbS 

.93  280 

969  789 

PbS04 

.73  586 

866798 

PbS 

PbS04 

.78  888 

897009 

TABLE  V  (CONTINUED) 


15 


Sought 

Found 

Factor 

log 

Pt 

NaCl 

1.66818 

222  243 

s 

BaSO. 

.13  738 

137  942 

As2S 

.39  092 

592  090 

S03- 

Ba§04 

.34  302 

535  313 

so 

BaSO. 

.41  156 

614431 

Sb 

Sb208 

.83  317 

920  734 

Sb204 

.78  928 

897  230 

Sb2S8 

.71360 

853  455 

SbS 

.59919 

777  568 

Sb208 

Sb204 

.94  732 

976  496 

Sb2S8 

.85  649 

932  721 

sb!s! 

.71  917 

856  834 

Si 

si625 

.46932 

671  469 

Si08 

Si02 

1.26534 

102  208 

SiO 

Si02 

1.53068 

184  885 

Si207 

Si02 

1.39800 

145  510 

Sn 

Sn02 

.78  808 

896570 

SnO 

SnO, 

.89  404 

951  357 

Sr 

SrCO, 

.59  354 

773  453 

SrO 

.84  558 

927  155 

SrS04 

.47  699 

678  507 

SrO 

SrC08 

.70  194 

846  298 

SrS04 

.56  409 

751352 

Ti 

Ti02 

.60  050 

778512 

U 

U02 

.88  166 

945  299 

W 

w3o38 

.84  820 
.79310 

928  497 
899330 

Zn 

ZnO 

.80  334 

904901 

ZnS 

.67  084 

826619 

ZnO 

ZnS 

.83  506 

921  718 

ZnS 

ZnO 

1.19752 

078  282 

16 


TABLE  VI 


REDUCTION  OF  BAROMETRIC  READINGS  TO  0° 

(For  temperatures  above  zero  the  corrections  are  negative  and  for  temperatures  below 

zero  positive.) 


Temper- 
ature 

Glass  Scale 

Brass  Scale 

740 

mm. 

750 

mm. 

760 

mm. 

770 

mm. 

780 

mm. 

740 

mm. 

750 

mm. 

760 

mm. 

770 
mm. 

780 

mm. 

0° 

0.00 

0.00 

0.00 

0.00 

0.00 

0.00 

0.00 

0.00 

0.00 

0.00 

1° 

13 

13 

13 

13 

14 

12 

12 

12 

13 

13 

2° 

26 

26 

26 

27 

27 

24 

25 

25 

25 

25 

3° 

38 

39 

39 

40 

41 

36 

37 

37 

38 

38 

4° 

51 

52 

53 

53 

54 

48 

49 

50 

50 

51 

5° 

0.64 

0.65 

0.66 

0.67 

0.68 

0.60 

0.61 

0.62 

0.63 

0.64 

6° 

77 

78 

79 

80 

81 

72 

73 

74 

75 

76 

7° 

0.90 

0.91 

0.92 

0.93 

0.95 

85 

86 

0.87 

0.88 

0.89 

8° 

1.02 

1.04 

1.05 

1.07 

1.08 

0.97 

0.98 

1.99 

1.01 

1.02 

9° 

15 

17 

18 

20 

21 

1.09 

1.10 

12 

13 

15 

10° 

1.28 

1.30 

1.31 

1.33 

1.35 

1.21 

1.22 

1.24 

1.26 

1.27 

11° 

41 

43 

45 

46 

48 

33 

35 

36 

38 

40 

12° 

53 

56 

58 

60 

62 

45 

47 

49 

51 

53 

13° 

66 

69 

71 

73 

75 

57 

59 

61 

63 

65 

14° 

79 

81 

84 

1.86 

1.89 

69 

71 

73 

76 

78 

15° 

1.92 

1.94 

1.97 

2.00 

2.02 

1.81 

1.83 

1.86 

1.88 

1.91 

16° 

2.05 

2.07 

2.10 

13 

16 

1.93 

1.96 

1.98 

2.01 

2.03 

17° 

17 

20 

23 

26 

29 

2.05 

2.08 

2.10 

13 

16 

18° 

30 

33 

36 

39 

43 

17 

20 

23 

26 

29 

19° 

43 

46 

49 

53 

56 

29 

32 

35 

38 

41 

20° 

2.56 

2.59 

2.62 

2.66 

2.69 

2.41 

2.44 

2.47 

2.51 

2.54 

21° 

68 

72 

76 

79 

83 

53 

56 

60 

63 

67 

22° 

81 

85 

2.89 

2.92 

2.96 

65 

69 

72 

76 

79 

23° 

2.94 

2.98 

3.02 

3.06 

3.10 

77 

81 

84 

2.88 

2.92 

24° 

3.06 

3.11 

15 

19 

23 

2.89 

2.93 

2.97 

3.01 

3.05 

25° 

3.19 

3.23 

3.28 

3.32 

3.36 

3.01 

3.05 

3.09 

3.13 

3.17 

26° 

32 

36 

41 

45 

50 

13 

17 

21 

26 

30 

27° 

45 

49 

54 

59 

63 

25 

29 

34 

38 

42 

28° 

57 

62 

67 

72 

77 

37 

41 

46 

51 

55 

29° 

70 

75 

80 

85 

3.90 

49 

54 

58 

63 

68 

30° 

3.83 

3.88 

3.93 

3.98 

4.03 

3.61 

3.66 

3.71 

3.75 

3.80 

31° 

3.95 

4.01 

4.06 

4.11 

17 

73 

78 

83 

3.88 

3.93 

32° 

4.08 

14 

19 

25 

30 

85 

3.90 

3.95 

4.00 

4.05 

33° 

21 

26 

32 

38 

43 

3.97 

4.02 

4.07 

13 

18 

34° 

33 

39 

45 

51 

57 

4.09 

14 

20 

25 

31 

35° 

4.46 

4.52 

4.58 

4.65 

4.71 

4.21 

4.26 

4.32 

4.38 

4.43 

TABLE  VII 


17 


GEOGRAPHICAL  LATITUDE,  ELEVATION,  AND  GRAVITY  (REFERRED  TO 
45°  AND  SEA  LEVEL)   OF  SOME  IMPORTANT  CITIES 


Latitude 

Height 
above 
sea  level 
m. 

Gravity 

log 

Baltimore,  Met. 

39°  18' 

23. 

0.9  994  705 

999  770 

Berlin,  New  Obs. 

52°  30'  16.7" 

37.00 

1.0006736 

000292 

Bonn,  Obs. 

50°  43'  45.0" 

61.92 

1.0005054 

000219 

Boston,  Met. 

42°  21' 

38. 

0.9  997  438 

999  889 

Brussels,  Old  Obs. 

50°  51'  10.7" 

56. 

1.0005179 

000225 

Cambridge,  Eng.,  Obs. 

52°  12'  5  1.6" 

28. 

1.0006504 

000282 

Cambridge,  Mass.,  Harvard  Obs. 

42°  22'  47.6" 

24. 

0.9  997  509 

999892 

Cincinnati,  Obs. 

39°    8'  19.5" 

263. 

0.9  993  803 

999731 

Dublin,  Dunsink  Obs. 

53°  23'  13.1" 

86. 

1.0007365 

000320 

Freiberg 

47°  59'  40" 

270.6 

1.0001907 

000083 

Gottingen,  Obs. 

51°  31'  48.2" 

159.2 

1.0005478 

000  238 

Greenwich,  Obs. 

51°  28'  38.1" 

47. 

1.0005783 

000251 

Heidelberg,  Obs. 

49°  23'  54.9" 

113.6 

1.0003688 

000  160 

Kopenhagen,  Obs. 

55°  41'  12.9" 

14. 

1.0009602 

000317 

London,  Camden  Sq.,  Met. 

51°  32'  30" 

34. 

1.0005881 

000  255 

Madrid,  Obs. 

45°  27'  59.2" 

120. 

1.0000053 

000  002 

Montreal,  McGill  Col.  Obs. 

45°  30'  17.0" 

57. 

1.0000287 

000012 

New  Haven,  Yale  Obs. 

41°  19'  22.3" 

32. 

0.9  996  521 

999  848 

New  Orleans,  Met. 

29°  58' 

16. 

0.9  986  721 

999423 

New  York,  Rutherford  Obs. 

40°  43'  48.5" 

96. 

0.9  995  774 

999817 

Paris,  Nat.  Obs. 

48°  50'  11.2" 

59. 

1.0  003  345 

000145 

Philadelphia,  Obs. 

39°  57'  7.5" 

36. 

0.9  995  254 

999  794 

Prag,  Obs. 

50°    5'  15.8" 

197. 

1.0004053 

000  176 

Quebec,  Obs. 

46°  48'  20.8" 

70. 

1.0001446 

000063 

St.  Louis,  Obs. 

38°38/3.6" 

171. 

0.9993611 

999  722 

San  Francisco,  Davidson  Obs. 

3  7°  4  r  28.0" 

47.2 

0.9  993  272 

999  708 

Strassburg,  New  Obs. 

48°  35'  0.3" 

144.66 

1.0002845 

000124 

Washington,  Georgetown  Hts.  Obs. 

38°  55'  14.  7" 

285. 

0.9993537 

999  719 

Zurich,  Obs.  d.  Polyt. 

47°  22'  40" 

468.24 

1.0000718 

000031 

18 


TABLE  VIII 


REDUCTION  OF  BAROMETRIC  READINGS  TO  NORMAL  GRAVITY 

(From  Landolt-Bornstein) 

A.   REDUCTION  TO  45°  LATITUDE 

(From  0°  to  45°  the  correction  is  always  negative,  and  from  45°  to  90°  positive.) 


Barometric  Readings  in  mm.,  corrected  for  Temperature 

Latitude 

640 

650 

660 

670 

680 

690 

700 

710 

720 

730 

740 

750 

760 

770 

780 

Latitude 

mm. 

mm. 

mm. 

mm. 

mm. 

mm. 

mm. 

mm. 

mm. 

mm. 

mm. 

mm. 

mm. 

mm. 

mm. 

0° 

1.66 

1.68 

1.71 

1.74 

1.76 

1.79 

1.81 

1.84 

1.86 

1.89 

1.92 

1.94 

1.97 

1.99 

2.02 

90° 

5° 

63 

66 

68 

71 

73 

76 

79 

81 

84 

86 

89 

91 

94 

96 

1.99 

85° 

10° 

56 

58 

61 

63 

65 

68 

70 

73 

75 

78 

80 

83 

85 

87 

90 

80° 

15° 

44 

46 

48 

50 

53 

55 

57 

59 

61 

64 

66 

68 

70 

73 

75 

75° 

20° 

27 

29 

31 

33 

35 

37 

39 

41 

43 

45 

47 

49 

51 

53 

55 

70° 

25° 

1.07 

1.08 

1.10 

1.12 

1.13 

1.15 

1.17 

1.18 

1.20 

1.22 

1.23 

1.25 

1.27 

28 

30 

65° 

30° 

0.83 

0.84 

0.85 

0.87 

0.88 

0.89 

0.91 

0.92 

0.93 

0.95 

0.96 

0.97 

0.98 

1.00 

1.01 

60° 

35° 

57 

58 

58 

59 

60 

61 

62 

63 

64 

65 

66 

66 

67 

0.68 

0.69 

55° 

40° 

29 

29 

30 

30 

31 

31 

31 

32 

32 

33 

33 

34 

34 

35 

35 

50° 

45° 

0.00 

0.00 

0.00 

0.00 

0.00 

0.00 

0.00 

0.00 

0.00 

0.00 

0.00 

0.00 

0.00 

0.00 

0.00 

45° 

B.   REDUCTION  TO  SEA  LEVEL 
(These  corrections  are  all  negative.) 


Height  above 
sea  level 

772. 

Barometric  Readings  in  mm.,  corrected  for  Temperature 

Height  above 
sea  level 

772. 

620 

772772. 

640 

mm. 

660 

mm. 

680 

mm. 

700 
mm. 

720 

mm. 

740 
mm. 

760 

mm. 

780 

mm. 

100 

0.01 

0.01 

0.01 

0.01 

0.02 

100 

200 

0.03 

03 

03 

03 

03 

0.03 

200 

300 

04 

04 

04 

04 

04 

300 

400 

0.05 

05 

05 

06 

06 

06 

400 

500 

06 

07 

07 

07 

07 

0.07 

500 

600 

08 

08 

08 

08 

09 

600 

700 

0.09 

09 

09 

10 

10 

10 

700 

800 

10 

10 

11 

11 

11 

0.12 

800 

900 

0.11 

0.12 

0.12 

0.12 

0.13 

900 

1000 

0.12 

0.13 

0.13 

0.13 

0.14 

0.14 

1000 

1100 

13 

14 

14 

15 

15 

0.16 

1100 

1200 

15 

15 

16 

16 

16 

1200 

1300 

16 

16 

17 

17 

18 

1300 

1400 

17 

18 

18 

19 

0.19 

1400 

1500 

18 

19 

19 

20 

1500 

1600 

19 

20 

21 

21 

1600 

1700 

21 

21 

22 

0.23 

1700 

1800 

22 

23 

23 

1800 

1900 

0.23 

0.24 

0.25 

1900 

2000 

0.24 

0.25 

2000 

TABLE  IX 


19 


CAPILLAKY  DEPRESSION  OF  MERCURY 

(Interpolated  by  F.  Kohlrausch  from  Mendelejeff  and  Gutkowsky.) 


Height  of  Meniscus  in  mm. 

Diameter 
of  tube 

0.4 

0.6 

0.8 

1.0 

1.2 

1.4 

1.6 

1.8 

mm. 

mm. 

mm. 

mm. 

mm. 

mm. 

mm. 

mm. 

mm. 

4 

0.83 

1.22 

1.54 

1.98 

2.37 

5 

47 

0.65 

0.86 

1.19 

1.45 

1.80 

6 

27 

41 

56 

0.78 

0.98 

1.21 

1.43 

7 

18 

28 

40 

53 

67 

0.82 

0.97 

1.13 

8 

20 

29 

38 

46 

56 

65 

0.77 

9 

15 

21 

28 

33 

40 

46 

52 

10 

15 

20 

25 

29 

33 

37 

11 

10 

14 

18 

21 

24 

27 

12 

07 

10 

13 

15 

18 

19 

13 

04 

07 

10 

12 

13 

14 

20 


TABLE  X 


TENSION  OF  AQUEOUS  VAPOR  OVER  WATER  — EXPRESSED  IN  TERMS 
OF  NORMAL  MERCURY  UNITS 

(Taken  from  Landolt-Bornstein.    Observations  by  Regnault.) 


Degrees 

Hydrogen  Scale.    Tenth  Degrees 

.0 

772/77. 

.1 

777771. 

.2 

777777. 

.3 

771772. 

.4 

777777. 

.5 

772772. 

.6 

777772. 

.7 

772777. 

.8 
mm. 

.9 

772772. 

0 

4.579 

4.612 

4.646 

4.679 

4.713 

4.747 

4.782 

4.816 

4.851 

4.886 

1 

4.921 

4.957 

4.992 

5.028 

5.064 

5.101 

5.137 

5.174 

5.211 

5.248 

2 

5.286 

5.324 

5362 

5.400 

5.438 

5.477 

5.516 

5.555 

5.595 

5.635 

3 

5.675 

5.715 

5.755 

5.796 

5.837 

5.878 

5.920 

5.961 

6.003 

6.046 

4 

6.088 

6.131 

6.174 

6.217 

6.261 

6.305 

6.349 

6.393 

6.438 

6.483 

5 

6.528 

6.574 

6.620 

6.666 

6.712 

6.759 

6.806 

6.853 

6.901 

6.949 

6 

6.997 

7.045 

7.094 

7.143 

7.192 

7.242 

7.292 

7.342 

7.392 

7.443 

7 

7.494 

7.546 

7.598 

7.650 

7.702 

7.755 

7.808 

7.861 

7.914 

7.968 

8 

8.023 

8.077 

8.132 

8.187 

8.243 

8.299 

8.355 

8.412 

8.469 

8.526 

9 

8.584 

8.642 

8.700 

8.759 

8.818 

8.877 

8.937 

8.997 

9.057 

9.118 

10 

9.179 

9.240 

9.302 

9.364 

9.427 

9.490 

9.553 

9.616 

9.680 

9.745 

11 

9.810 

9.875 

9.940 

10.006 

10.072 

10.139 

10.206 

10.274 

10.342 

10.410 

12 

10.479 

10.548 

10.617 

10.687 

10.757 

10.828 

10.899 

10.970 

11.042 

11.114 

13 

11.187 

11.260 

11.333 

11.407 

11.481 

11.556 

11.631 

11.706 

11.782 

11.859 

14 

11.936 

12.013 

12.091 

12.169 

12.247 

12.326 

12.406 

12.486 

12.566 

12.647 

15 

12.728 

12.810 

12.892 

12.974 

13.057 

13.141 

13.225 

13.309 

13.394 

13.480 

16 

13.565 

13.651 

13.738 

13.825 

13.913 

14.001 

14.090 

14.179 

14.269 

14.359 

17 

14.450 

14.541 

14.632 

14.724 

14.817 

14.910 

15.003 

15.097 

15.192 

15.287 

18 

15.383 

15.479 

15.575 

15.672 

15.770 

15.858 

15.967 

16.066 

16.166 

16.266 

19 

16.367 

16.469 

16.571 

16.673 

16.776 

16.8SO 

16.984 

17.088 

17.193 

17.299 

20 

17.406 

17.513 

17.620 

17.728 

17.837 

17.947 

18.057 

18.167 

18.278 

18.390 

21 

18.503 

18.616 

18.729 

18.844 

18.959 

19.074 

19.190 

19.307 

19.424 

19.542 

22 

19.661 

19.780 

19.900 

20.021 

20.142 

20.264 

20.386 

20.510 

20.634 

20.758 

23 

20.883 

21.010 

21.137 

21.264 

21.393 

21.522 

21.652 

21.782 

21.913 

22.045 

24 

22.178 

22.311 

22.446 

22.581 

22.716 

22.853 

22.990 

23.128 

23.266 

23.406 

25 

23.546 

23.686 

23.828 

23.970 

24.113 

24.257 

24.401 

24.547 

24.693 

24.839 

26 

24.987 

25.135 

25.284 

25.434 

25.584 

25.736 

25.888 

26.041 

26.195 

26.349 

27 

26.505 

26.661 

26.818 

26.976 

27.134 

27.294 

27.454 

27.615 

27.777 

27.939 

28 

28.103 

28.267 

28.432 

28.599 

28.766 

28.933 

29.102 

29.271 

29.442 

29.613 

29 

29.785 

29.958 

30.132 

30.307 

30.482 

30.659 

30.836 

31.015 

31.194 

31.374 

30 

31.555 

31.737 

31.919 

32.103 

32.288 

32.473 

32.660 

32.847 

33.036 

33.225 

31 

33.416 

33.607 

33.799 

33.992 

34.187 

34.382 

34.578 

34.775 

34.973 

35.172 

32 

35.372 

35.573 

35.775 

35.978 

36.182 

36.387 

36.593 

36.800 

37.008 

37.217 

33 

37.427 

37.638 

37.851 

38.064 

38.278 

38.493 

38.710 

38.927 

39.146 

39.365 

34 

39.586 

39.807 

40.030 

40.254 

40.479 

40.705 

40.933 

41.161 

41.390 

41.621 

35 

41.853 

42.085 

42.319 

42.554 

42.791 

43.028 

43.266 

43.506 

43.747 

43.989 

TABLE  XI 


21 


REDUCTION  OF  WATER  PRESSURE  TO  MERCURY  PRESSURE 

(Calculated  from  the  following :  temperature  of  the  water  4°,  of  the  mercury  0° ; 
density  of  the  water  1,  of  the  mercury  13.59545) 

(Thiesen  and  Schul.  Z.  S.  f .  Instrk.  18,  138) 


Water 

Mercury 

Water 

Mercury 

Water 

Mercury 

Water 

Mercury 

Water 

Mercury 

10 

0.74 

50 

3.68 

90 

6.62 

130 

9.56 

170 

12.50 

11 

81 

51 

75 

91 

69 

131 

64 

171 

58 

12 

88 

52 

82 

92 

77 

132 

71 

172 

65 

13 

0.96 

53 

90 

93 

84 

133 

78 

173 

72 

14 

1.03 

54 

3.97 

94 

91 

134 

86 

174 

80 

15 

10 

55 

4.05 

95 

6.99 

135 

9.93 

175 

87 

16 

18 

56 

12 

96 

7.06 

136 

10.00 

176 

12.95 

17 

25 

57 

19 

97 

13 

137 

08 

177 

13.02 

18 

32 

58 

27 

98 

21 

138 

15 

178 

09 

19 

40 

59 

34 

99 

28 

139 

22 

179 

17 

20 

1.47 

60 

4.41 

100 

7.36 

140 

10.30 

180 

13.24 

21 

54 

61 

49 

101 

43 

141 

37 

181 

31 

22 

62 

62 

56 

102 

50 

142 

44 

182 

38 

23 

69 

63 

63 

103 

58 

143 

52 

183 

46 

24 

77 

64 

71 

104 

65 

144 

59 

184 

53 

25 

84 

65 

78 

105 

72 

145 

67 

185 

61 

26 

91 

66 

85 

106 

80 

146 

74 

186 

68 

27 

1.99 

67 

4.93 

107 

87 

147 

81 

187 

75 

28 

2.06 

68 

5.00 

108 

7.94 

148 

89 

188 

83 

29 

13 

69 

08 

109 

8.02 

149 

10.96 

189 

90 

30 

2.21 

70 

5.15 

110 

8.09 

150 

11.03 

190 

13.98 

31 

28 

71 

22 

111 

16 

151 

11 

191 

14.05 

32 

35 

72 

30 

112 

24 

152 

18 

192 

12 

33 

43 

73 

37 

113 

31 

153 

25 

193 

20 

34 

50 

74 

44 

114 

39 

154 

33 

194 

27 

35 

57 

75 

52 

115 

46 

155 

40 

195 

34 

36 

65 

76 

59 

116 

53 

156 

47 

196 

42 

37 

72 

77 

66 

117 

61 

157 

55 

197 

49 

38 

79 

78 

74 

118 

68 

158 

62 

198 

56 

39 

87 

79 

81 

119 

75 

159 

69 

199 

64 

40 

2.94 

80 

5.88 

120 

8.83 

160 

11.77 

200 

14.71 

41 

3.02 

81 

5.96 

121 

90 

161 

84 

300 

22.07 

42 

09 

82 

6.03 

122 

8.97 

162 

92 

400 

29.42 

43 

16 

83 

10 

123 

9.05 

163 

11.99 

500 

36.78 

44 

24 

84 

18 

124 

12 

164 

12.06 

600 

44.13 

45 

31 

85 

25 

125 

19 

165 

14 

700 

51.49 

46 

38 

86 

33 

126 

27 

166 

21 

800 

58.84 

47 

46 

87 

40 

127 

34 

167 

28 

900 

66.20 

48 

53 

88 

47 

128 

41 

168 

36 

1000 

73.55 

49 

60 

89 

55 

129 

49 

169 

43 

TABLE  XII 


REDUCTION  OF  THE  VOLUME  OF  GASES  TO  NORMAL  PRESSURE 
(This  table  contains  the  values  of  —  where  h  =  500  to  839  mm.) 

t \)\) 

(Landolt-Bb'rnstein) 


h 
mm. 

h 
760 

log  — 
6  760 

h 
nun. 

h 
760 

10g4 

h 
mm. 

h 
760 

log  — 
6  760 

500 

0.65  789 

818153 

540 

0.71  053 

851  582 

580 

0.76316 

882  616 

501 

0.65  921 

9024 

541 

184 

2382 

581 

447 

3360 

502 

0.66  053 

819  893 

542 

316 

3187 

582 

579 

4110 

503 

184 

820  753 

543 

447 

3984 

583 

711 

4  858 

504 

316 

1618 

544 

579 

4786 

584 

842 

5599 

505 

447 

2475 

545 

711 

5586 

585 

0.76974 

6344 

506 

579 

3337 

546 

842 

6378 

586 

0.77  105 

7083 

507 

711 

4198 

547 

0.71  974 

7176 

587 

237 

7825 

508 

842 

5049 

548 

0.72  105 

7965 

588 

368 

8561 

509 

0.66974 

5906 

549 

237 

8760 

589 

500 

889  302 

510 

0.67  105 

826  755 

550 

0.72  368 

859  547 

590 

0.77  632 

890041 

511 

237 

7608 

551 

500 

860  338 

591 

763 

0773 

512 

368 

8454 

552 

632 

1128 

592 

0.77  895 

1510 

513 

500 

829304 

553 

763 

1911 

593 

0.78026 

1682 

514 

632% 

830  152 

554 

0.72  895 

2698 

594 

158 

2973 

515 

763 

0993 

555 

0.73  026 

3478 

595 

289 

3701 

516 

0.67  895 

1838 

556 

158 

4262 

596 

421 

4432 

517 

0.68  026 

2675 

557 

289 

5039 

597 

553 

5163 

518 

158 

3517 

558 

421 

5820 

598 

684 

5886 

519 

289 

4351 

559 

553 

6600 

599 

816 

6614 

520 

0.68421 

835  189 

560 

0.73  684 

867373 

600 

0.78  947 

897  336 

521 

553 

6027 

561 

816 

8151 

601 

0.79  079 

8061 

522 

684 

6856 

562 

0.73  947 

8921 

602 

211 

8786 

523 

816 

7689 

563 

0.74  079 

869  695 

603 

342 

899  503 

524 

0.68  947 

8515 

564 

211 

870  468 

604 

474 

900  225 

525 

0.69  079 

839346 

565 

342 

1234 

605 

605 

0940 

526 

211 

840  175 

566 

474 

2005 

606 

737 

1660 

527 

342 

0996 

567 

605 

2768 

607 

0.79868 

2373 

528 

474 

1822 

568 

737 

3536 

608 

0.80000 

3090 

529 

605 

2640 

569 

0.74  868 

4296 

609 

132 

3806 

530 

0.69  737 

843  463 

570 

0.75  000 

875  061 

610 

0.80  263 

904515 

531 

0.69  868 

4278 

571 

132 

5825 

611 

395 

5229 

532 

0.70  000 

5098 

572 

263 

6582 

612 

526 

•  5936 

533 

132 

5916 

573 

395 

7343 

613 

658 

6647 

534 

263 

6727 

574 

526 

8097 

614 

789 

7352 

535 

395 

7542 

575 

658 

8855 

615 

0.80  921 

8061 

536 

526 

8349 

576 

789 

879  606 

616 

0.81  053 

8769 

537 

658 

9161 

577 

0.75  921 

880  362 

617 

184 

909470 

538 

789 

849  966 

578 

0.76  053 

1  116 

618 

316 

910  176 

539 

921 

850  775 

579 

184 

1864 

619 

447 

0875 

TABLE  XII  (CONTINUED) 


23 


h 
mm. 

h 
760 

log  — 
6  760 

h 
mm. 

h 
760 

iogA 

6  760 

h 
mm. 

h 
760 

icgA 

6  760 

620 

0.81  579 

911  578 

660 

0.86  842 

938  730 

700 

0.92  105 

964  283 

621 

711 

2281 

661 

0.86  974 

939  389 

701 

237 

4905 

622 

842 

2976 

662 

0.87  105 

940043 

702 

368 

5522 

623 

0.81  974 

3676 

663 

237 

0701 

703 

500 

6142 

624 

0.82  105 

4370 

664 

368 

1352 

704 

632 

6761 

625 

237 

5067 

665 

500 

2008 

705 

763 

7375 

626 

368 

5759 

666 

632 

2663 

706 

0.92  895 

7992 

627 

500 

6454 

667 

763 

3312 

707 

0.93  026 

8604 

628 

632 

7148 

668 

0.87  895 

3964 

708 

158 

9220 

629 

763 

7836 

669 

0.88026 

4611 

709 

289 

969  830 

630 

0.82  895 

918528 

670 

O.SS  158 

945  262 

710 

0.93  421 

970  445 

631 

0.83  026 

9214 

671 

289 

5907 

711 

553 

1058 

632 

158 

919  904 

672 

421 

6555 

712 

684 

1665 

633 

289 

920  588 

673 

553 

7203 

713 

816 

2277 

634 

421 

1275 

674 

684 

7845 

714 

0.93  947 

2883 

635 

553 

1962 

675 

816 

8491 

715 

0.94  079 

3493 

636 

684 

2642 

676 

0.88  947 

9131 

716 

211 

4102 

637 

816 

3327 

677 

0.89  079 

949  775 

717 

342 

4705 

638 

0.83  947 

4005 

678 

211 

950418 

718 

474 

5312 

639 

0.84079 

4688 

679 

342 

1056 

719 

605 

5914 

640 

0.84211 

925  369 

680 

0.89  474 

951  697 

720 

0.94  737 

976  520 

641 

342 

6044 

681 

605 

2332 

721 

0.94  868 

7120 

642 

474 

6723 

682 

737 

2972 

722 

0.95  000 

7724 

643 

605 

7396 

683 

0.89  868 

3605 

723 

132 

8327 

644 

737 

8073 

684 

0.90000 

4243 

724 

263 

8924 

645 

0.84  868 

8744 

685 

132 

4879 

725 

394 

979  521 

646 

0.85  000 

929  419 

686 

263 

5510 

726 

526 

980  122 

647 

132 

930  093 

687 

395 

6144 

727 

658 

0721 

648 

263 

0761 

688 

526 

6773 

728 

789 

1316 

649 

395 

1432 

689 

658 

7406 

729 

0.95  921 

1914 

650 

0.85  526 

932  098 

690 

0.90  789 

958  033 

730 

0.96  053 

982511 

651 

658 

2768 

691 

0.90921 

8664 

731 

184 

3103 

652 

790 

3437 

692 

0.91  053 

9294 

732 

316 

3698 

653 

0.85  921 

4099 

693 

184 

959919 

733 

447 

4289 

654 

0.86053 

4766 

694 

316 

960547 

734 

579 

4883 

655 

184 

5427 

695 

447 

1  170 

735 

710 

5471 

656 

316 

6091 

696 

579 

1796 

'736 

842 

6064 

657 

447 

6750 

697 

711 

2421 

737 

0.96  974 

6655 

658 

579 

7413 

698 

842 

3041 

738 

0.97  105 

7242 

659 

711 

8074 

699 

974 

3665 

739 

237 

7832 

24 


TABLE  XII  (CONTINUED) 


h 
mm. 

h 
760 

log  — 
760 

h 
mm. 

h 
760 

log  — 
760 

h 
mm. 

h 
760 

10g4 

740 

0.97  368 

988  416 

780 

1.02  632 

Oil  283 

820 

1.07  895 

033  001 

741 

500 

9005 

781 

763 

1837 

821 

1.08026 

3529 

742 

632 

989  592 

782 

1.02  895 

2394 

822 

158 

4059 

743 

763 

990  175 

783 

1.03026 

2947 

823 

289 

4584 

744 

0.97  895 

0761 

784 

158 

3504 

824 

421 

5  113 

745 

0.98  026 

1341 

785 

289 

4054 

825 

553 

5642 

746 

158 

1926 

786 

421 

4609 

826 

684 

6166 

747 

289 

2505 

787 

553 

5163 

827 

816 

6693 

748 

421 

3088 

788 

684 

5712 

828 

1.08  947 

7215 

749 

553 

3670 

789 

816 

6264 

829 

1.09  079 

7741 

750 

0.98  684 

994  247 

790 

1.03947 

016812 

830 

1.09211 

038  267 

751 

816 

4827 

791 

1.04079 

7363 

831 

342 

8787 

752 

0.98  947 

5403 

792 

211 

7914 

832 

471 

9299 

753 

0.99079 

5982 

793 

342 

8459 

833 

605 

039  831 

754 

211 

6560 

794 

474 

9008 

834 

737 

040  353 

755 

342 

7133 

795 

605 

019552 

835 

1.09  868 

0871 

756 

474 

7710 

796 

737 

020  100 

836 

1.10000 

1393 

757 

605 

8281 

797 

1.04868 

0643 

837 

132 

1913 

758 

737 

8856 

798 

1.05  000 

1  189 

838 

263 

2430 

759 

0.99  868 

999  426 

799 

132 

1  735 

839 

395 

2949 

760 

1.00000 

000000 

800 

1.05  263 

022  276 

761 

1.00  132 

0573 

801 

395 

2820 

762 

263 

1  141 

802 

526 

3359 

763 

392 

1699 

803 

658 

3902 

764 

526 

2278 

804 

789 

4441 

765 

658 

2848 

805 

1.05921 

4982 

766 

789 

3413 

806 

1.06053 

5523 

767 

1.00  921 

3982 

807 

184 

6059 

768 

1.01  053 

4549 

808 

316 

6598 

769 

184 

5112 

809 

447 

7134 

770 

1.01316 

005  678 

810 

1.06  579 

027  672 

771 

447 

6239 

811 

711 

8209 

772 

579 

6804 

812 

842 

8742 

773 

710 

7364 

813 

1.06974 

9278 

774 

842 

7927 

814 

1.07  105 

029  809 

775 

1.01  974 

8489 

815 

237 

030  345 

776 

1.02  105 

9047 

816 

368 

0875 

777 

237 

009  608 

817 

500 

1408 

778 

368 

010  164 

818 

632 

1941 

779 

500 

0724 

819 

763 

2470 

TABLE  XIII 


25 


REDUCTION  OF  THE  VOLUME  OF  GASES  TO  0°C. 


This  table  contains  the  logarithms  of  the  values  of 


1  +  0.003670 1 


where  t  —  0  to  149°. 


t 

log 

t 

log 

t 

log 

t 

log 

0.0 

000000 

4.0 

993671 

8.0 

987433 

12.0 

981  284 

0.1 

999  839 

4.1 

3513 

8.1 

7277 

12.1 

1130 

0.2 

9683 

4.2 

3359 

8.2 

7  125 

12.2 

0980 

0.3 

9523 

4.3 

3200 

8.3 

6969 

12.3 

0826 

0.4 

9  362 

4.4 

3042 

8.4 

6813 

12.4 

0672 

0.5 

9202 

4.5 

2884 

8.5 

6657 

12.5 

0518 

0.6 

9  045 

4.6 

2730 

8.6 

6505 

12.6 

0368 

0.7 

8885 

4.7 

2572 

8.7 

6350 

12.7 

0215 

0.8 

8725 

4.8 

2414 

8.8 

6194 

12.8 

980062 

0.9 

8569 

4.9 

2260 

8.9 

6043 

12.9 

979  912 

1.0 

998  409 

5.0 

992  103 

9.0 

985  888 

13.0 

979  759 

1.1 

8249 

5.1 

1945 

9.1 

5732 

13.1 

9606 

1.2 

8093 

5.2 

1  792 

9.2 

5581 

13.2 

9457 

1.3 

7934 

5.3 

1634 

9.3 

5425 

13.3 

9304 

1.4 

7774 

5.4 

1477 

9.4 

5270 

13.4 

9150 

1.5 

7618 

5.5 

1323 

9.5 

5  119 

13.5 

9002 

1.6 

7458 

5.6 

1166 

9.6 

4963 

13.6 

8848 

1.7 

7304 

5.7 

1008 

9.7 

4808 

13.7 

8695 

1.8 

7137 

5.8 

0850 

9.8 

4  653 

13.8 

8542 

1.9 

6984 

5.9 

0697 

9.9 

4502 

13.9 

8393 

2.0 

996824 

•  6.0 

990540 

10.0 

984  347 

14.0 

978  240 

2.1 

6664 

6.1 

0383 

10.1 

4  192 

14.1 

8087 

2.2 

6509 

6.2 

0231 

10.2 

4041 

14.2 

7938 

2.3 

6350 

6.3 

990073 

10.3 

3887 

14.3 

7786 

2.4 

6191 

6.4 

989  916 

10.4 

3732 

14.4 

7634 

2.5 

6032 

6.5 

9759 

10.5 

3577 

14.5 

7481 

2.6 

5877 

6.6 

9607 

10.6 

3426 

14.6 

7333 

2.7 

5718 

6.7 

9450 

10.7 

3271 

14.7 

7180 

2.8 

5559 

6.8 

9293 

10.8 

3117 

14.8 

7028 

2.9 

5404 

6.9 

9141 

10.9 

2967 

14.9 

6880 

3.0 

995  244 

7.0 

988983 

11.0 

982  813 

15.0 

976  727 

3.1 

5086 

7.1 

8828 

11.1 

2658 

15.1 

6575 

3.2 

4931 

7.2 

8675 

11.2 

2507 

15.2 

6427 

3.3 

4772 

7.3 

8519 

11.3 

2353 

15.3 

6274 

3.4 

4614 

7.4 

8362 

11.4 

2199 

15.4 

6122 

3.5 

4459 

7.5 

8210 

11.5 

2049 

15.5 

5974 

3.6 

4301 

7.6 

8054 

11.6 

1895 

15.6 

5822 

3.7 

4142 

7.7 

7897 

11.7 

1  741 

15.7 

5665 

3.8 

3984 

7.8 

7741 

11.8 

1587 

15.8 

5517 

3.9 

3829 

7.9 

7588 

11.9 

1437 

15.9 

5370 

2(3 


TABLE  XIII  (CONTINUED) 


t 

log 

t 

log 

t 

log 

t 

log 

16.0 

975  229 

20.0 

969  238 

24.0 

963  339 

28.0 

957519 

16.1 

5067 

20.1 

9089 

24.1 

3192 

28.1 

7373 

16.2 

4919 

20.2 

8943 

24.2 

3048 

28.2 

7236 

16.3 

4768 

20.3 

8794 

24.3 

2900 

28.3 

7095 

16.4 

4616 

20.4 

8644 

24.4 

2753 

28.4 

6941 

16.5 

4465 

20.5 

8495 

24.5 

2606 

28.5 

6795 

16.6 

4318 

20.6 

8350 

24.6 

2462 

28.6 

6654 

16.7 

4166 

20.7 

8200 

24.7 

2315 

28.7 

6508 

16.8 

4015 

20.8 

8051 

24.8 

2167 

288 

6363 

16.9 

3867 

20.9 

7905 

24.9 

2024 

28.9 

6221 

17.0 

973  717 

21.0 

967  756 

25.0 

961  876 

29.0 

956  076 

17.1 

3565 

21.1 

7606 

25.1 

1  729 

29.1 

5931 

17.2 

3418 

21.2 

7461 

25.2 

1586 

29.2 

5789 

17.3 

3267 

21.3 

7313 

25.3 

1440 

29.3 

5644 

17.4 

3116 

21.4 

7164 

25.4 

1293 

29.4 

5499 

17.5 

2968 

21.5 

7019 

25.5 

1  150 

29.5 

5358 

17.6 

2817 

21.6 

6870 

25.6 

1003 

29.6 

5213 

17.7 

2666 

21.7 

6721 

25.7 

0856 

29.7 

5068 

17.8 

2516 

21.8 

6572 

25.8 

0709 

29.8 

4923 

17.9 

2369 

21.9 

6427 

25.9 

0566 

29.9 

4783 

18.0 

972  219 

22.0 

966  279 

26.0 

960419 

30.0 

954  638 

18.1 

2068 

22.1 

6130 

26.1 

0272 

30.1 

4493 

18.2 

1922 

22.2 

5986 

26.2 

960  130 

30.2 

4353 

18.3 

1771 

22.3 

5837 

26.3 

959  983 

30.3 

4208 

18.4 

1620 

22.4 

5689 

26.4 

9837    ' 

30.4 

4063 

18.5 

1470 

22.5 

5541 

26.5 

9690 

30.5 

3918 

18.6 

1323 

22.6 

5396 

26.6 

9548 

30.6 

3778 

18.7 

1173 

22.7 

5248 

26.7 

9402 

30.7 

3634 

18.8 

1022 

22.8 

5099 

26.8 

9255 

30.8 

3489 

18.9 

0876 

22.9 

4955 

26.9 

9113 

30.9 

3349 

19.0 

970  726 

23.0 

964  807 

27.0 

958  966 

31.0 

953  205 

19.1 

0575 

23.1 

4658 

27.1 

8820 

31.1 

3060 

19.2 

0430 

23.2 

4514 

27.2 

8678 

31.2 

2920 

19.3 

0280 

23.3 

4366 

27.3 

8532 

31.3 

2776 

19.4 

970  130 

23.4 

4218 

27.4 

8387 

31.4 

2632 

19.5 

969  981 

23.5 

4074 

27.5 

8245 

31.5 

2492 

19.6 

9829 

23.6 

3926 

27.6 

8099 

31.6 

2348 

197 

9682 

28.7 

3778 

27.7 

7953 

31.7 

2204 

19.8 

9534 

23.8 

3630 

27.8 

7806 

31.8 

2060 

19.9 

9388 

23.9 

3487 

27.9 

7664 

31.9 

1920 

TABLE  XIII  (CONTINUED) 


27 


t 

log 

t 

log 

t 

log 

t 

log 

32.0 

951  776 

35 

947518 

70 

900700 

110 

852  726 

32.1 

1632 

36 

6114 

71 

899  433 

111 

1592 

32.2 

1492 

37 

4702 

72 

8170 

112 

850  461 

32.3 

1349 

38 

3303 

73 

6912 

113 

849  333 

32.4 

1205 

39 

1905 

74 

5656 

114 

8208 

32.5 

1061 

75 

4405 

115 

7085 

32.6 

0922 

76 

3156 

116 

5965 

32.7 

0778 

77 

1912 

117 

4849 

32.8 

0635 

78 

0671 

118 

3736 

32.9 

0495 

79 

889  434 

119 

2625 

33.0 

950351 

40 

940513 

80 

888  200 

120 

841  517 

33.1 

0208 

41 

939  125 

81 

6970 

121 

840412 

33.2 

950  069 

42 

7741 

82 

5743 

122 

839  309 

33.3 

949  926 

43 

6363 

83 

4519 

123 

8210 

33.4 

9783 

44 

4988 

84 

3  299 

124 

7113 

33.5 

9643 

45 

3618 

85 

2083 

125 

6019 

33.6 

9500 

46 

2252 

86 

880  869 

126 

4928 

33.7 

9358 

47 

930  891 

87 

879  660 

127 

3839 

33.8 

9215 

48 

9  534 

88 

8453 

128 

2754 

33.9 

9075 

49 

8181 

89 

7250 

129 

1671 

34.0 

948  932 

50 

926832 

90 

876  050 

130 

830  591 

51 

5487 

91 

4854 

131 

829513 

52 

4147 

92 

3661 

132 

8438 

53 

2810 

93 

2471 

133 

7365 

54 

1478 

94 

1284 

134 

6295 

55 

920150 

95 

870  101 

135 

5228 

56' 

918  826 

96 

868  920 

136 

4164 

57 

7506 

97 

7743 

137 

3102 

58 

6189 

98 

6570 

138 

2043 

59 

4877 

99 

5399 

139 

820  986 

60 

913  569 

100 

864  231 

140 

819932 

61 

2265 

101 

3067 

141 

8880 

62 

910964 

102 

1906 

142 

7831 

63 

909  668 

103 

860  748 

143 

6784 

64 

8375 

104 

859  593 

144 

5741 

65 

7087 

105 

8441 

145 

4699 

66 

5801 

106 

7292 

146 

3660 

67 

4520 

107 

6146 

147 

2623 

68 

3243 

108 

5003 

148 

1589 

69 

1969 

109 

3863 

149 

0558 

28 


TABLE  XIV 


REDUCTION  OF  THE  VOLUME  OF  GASES  SATURATED  WITH  AQUEOUS 
VAPOR  TO  0°,  NORMAL  PRESSURE,  AND  DRY 


(1  +  0.003070^)700 

(V  is  the  volume  of  the  gas,  p  the  uncorrected  barometric  pressure  read  on  a  glass  or 
wooden  scale,  p0  barometric  pressure  corrected  for  temperature,  h  the  maximum  tension 
of  aqueous  vapor,  t  the  temperature.  This  table  contains  the  logarithms  of 


(1  +  0.008670*)  760 

where  p  varies  from  730  to  780  and  t  from  12°  to  24°.) 

(Landolt-Bornstein) 


t 

p=730 

log 

Differ- 
ence 
for 
10mm. 

p  =  740 

log 

Differ- 
ence 
for 
10mm. 

p=750 
log 

Differ- 
ence 
for 
10mm. 

p=760 
log 

Differ- 
ence 
for 
10mm. 

p=770 
log 

Differ- 
ence 
for 
10mm. 

p  =  780 
log 

12.0 

95663 

599 

96262 

591 

96  853 

584 

97437 

575 

98012 

568 

98  580 

12.2 

622 

600 

222 

591 

813 

583 

396 

576 

97972 

568 

540 

12.4 

582 

599 

181 

592 

773 

583 

356 

576 

932 

568 

500 

12.6 

541 

600 

141 

592 

733 

583 

316 

576 

892 

568 

460 

12.8 

501 

599 

100 

592 

692 

584 

276 

576 

852 

568 

420 

13.0 

95460 

600 

96060 

592 

96652 

584 

97236 

'  576 

97812 

568 

98380 

13.2 

419 

600 

96019 

592 

611 

584 

195 

576 

771 

569 

340 

13.4 

378 

601 

95979 

592 

571 

584 

155 

576 

731 

569 

300 

13.6 

337 

601 

938 

592 

530 

584 

114 

577 

691 

568 

259 

13.8 

296 

601 

897 

592 

489 

584 

073 

577 

650 

569 

219 

14.0 

95  256 

600 

95856 

592 

96448 

585 

97033 

576 

97609 

570 

98179 

14.2 

214 

601 

815 

592 

407 

585 

96992 

577 

569 

569 

138 

14.4 

173 

601 

774 

592 

366 

585 

951 

577 

528 

569 

097 

14.6 

131 

601 

732 

593 

325 

585 

910 

577 

487 

570 

057 

14.8 

090 

601 

691 

593 

284 

585 

869 

577 

446 

570 

016 

15.0 

95048 

602 

95650 

593 

96243 

585 

96828 

577 

97405 

570 

97  975  . 

15.2 

95007 

601 

608 

593 

201 

585 

786 

578 

364 

570 

934 

15.4 

94965 

601 

566 

594 

160 

585 

745 

578 

323 

570 

893 

15.6 

923 

602 

525 

593 

118 

586 

704 

577 

281 

570 

851 

15.8 

881 

602 

483 

594 

077 

585 

662 

578 

240 

570 

810 

16.0 

94839 

602 

95441 

594 

96035 

585 

96620 

578 

97198 

571 

97  769 

16.2 

797 

602 

399 

594 

95993 

586 

579 

578 

157 

570 

727 

16.4 

755 

602 

357 

594 

951 

586 

537 

578 

115 

571 

686 

16.6 

712 

603 

315 

594 

909 

586 

495 

578 

073 

571 

644 

16.8 

670 

602 

272 

595 

867 

586 

453 

579 

032 

570 

602 

TABLE  XIV  (CONTINUED) 


29 


t 

p  =  730 

log 

Differ- 
ence 
for 
10mm. 

p  =  740 

log 

Differ- 
ence 
for 
10mm. 

p  =  750 

log 

Differ- 
ence 
for 
10mm. 

p  =  760 

log 

Differ- 
ence 
for 
10mm. 

p  =  770 
log 

Differ- 
ence 
for 
10mm. 

p  =  780 
log 

17.0 

94627 

603 

95230 

594 

95824 

587 

96411 

579 

96990 

571 

97561 

17.2 

585 

602 

187 

595 

782 

587 

369 

578 

947 

572 

519 

17.4 

542 

603 

145 

595 

740 

586 

326 

579 

905 

572 

477 

17.6 

499 

603 

102 

595 

697 

587 

284 

579 

863 

571 

434 

17.8 

456 

603 

059 

595 

654 

587 

241 

580 

821 

571 

392 

18.0 

94413 

603 

95  016 

596 

95612 

587 

96  199 

579 

96778 

572 

97  350 

18.2 

370 

603 

94973 

596 

569 

587 

156 

580 

736 

571 

307 

18.4 

326 

604 

930 

596 

526 

587 

113 

580 

693 

572 

265 

18.6 

283 

604 

887 

596 

483 

587 

070 

580 

650 

572 

222 

18.8 

239 

604 

843 

596 

439 

588 

027 

580 

607 

573 

180 

19.0 

94196 

604 

94800 

596 

95396 

588 

95984 

580 

96564 

573 

97137 

19.2 

152 

604 

756 

597 

353 

588 

941 

580 

521 

573 

094 

19.4 

108 

605 

713 

596 

309 

588 

897 

581 

478 

573 

051 

19.6 

064 

605 

669 

596 

265 

589 

854 

580 

434 

573 

97007 

19.8 

020 

605 

625 

596 

221 

589 

810 

581 

391 

573 

96964 

20.0 

93975 

606 

94  581 

597 

95178 

588 

95766 

581 

96347 

574 

96921 

20.2 

931 

605 

536 

597 

133 

589 

722 

582 

304 

573 

877 

20.4 

886 

606 

492 

597 

089 

589 

678 

582 

260 

573 

833 

20.6 

842 

606 

448 

597 

045 

589 

634 

582 

216 

574 

790 

20.8 

797 

606 

403 

598 

001 

589 

590 

582 

172 

574 

746 

21.0 

93752 

606 

94358 

598 

94  956 

590 

95546 

581 

96127 

575 

96702 

21.2 

707 

606 

313 

598 

911 

590 

501 

582 

083 

574 

.657 

21.4 

662 

606 

268 

598 

866 

591 

457 

582 

96039 

574 

613 

21.6 

616 

607 

223 

598 

821 

591 

412 

582 

95994 

575 

569 

21.8 

571 

607 

178 

598 

776 

591 

367 

582 

949 

575 

524 

22.0 

93  525 

607 

94132 

599 

94  731 

591 

95322 

583 

95  905 

575 

96480 

22.2 

479 

608 

087 

599 

686 

591 

277 

583 

860 

575 

435 

22.4 

433 

608 

94041 

599 

640 

591 

231 

583 

814 

576 

390 

22.6 

387 

608 

93  995 

600 

595 

591 

186 

583 

769 

576 

345 

22.8 

341 

60S 

949 

600 

549 

591 

140 

584 

724 

575 

299 

23.0 

93295 

608 

93903 

600 

94503 

591 

95094 

584 

95678 

576 

96254 

23.2 

248 

609 

857 

600 

457 

592 

049 

583 

632 

577 

209 

23.4 

202 

608 

810 

601 

411 

592 

95003 

584 

587 

576 

163 

23.6 

155 

609 

764 

600 

364 

592 

94956 

585 

541 

576 

117 

23.8 

108 

609 

717 

601 

318 

592 

910 

585 

495 

576 

071 

24.0 

93061 

609 

93670 

601 

94271 

593 

94864 

584 

95448 

577 

96025 

30 


TABLE  X\7 


OBSERVED  DENSITY  AND  THE  WEIGHT  OF  A  LITER  OF  SOME  COMMON 

GASES  UNDER  THE  FOLLOWING  CONDITIONS  :   0°  AND   760  MM.  PRESSURE 

AT  SEA  LEVEL  AND  45°  LATITUDE.    AIR  =  1 


Substance 

Density 

Wt.  1  liter 
in  grams 
at  sea  level 
and  45°  lat. 

log 

Observer 

Acetylene 

0.92 

1.1620 

065  206 

Berthelot 

Air 

1.00 

1.2928 

111532 

Leduc                "1  Mean 
Lord  Rayleigh  J  value 

Ammonia 

0.5971 

0.7621 

882  012 

Leduc 

Argon 

1.379 

1.782 

250  908 

Ramsay  and  Travers 

Bromine 

f   5.5243     1 
\  at  227.92°  J 

7.1426 

853  856 

Jahn 

Carbon  dioxide 

1.52909 

1.9652 

293  407 

Lord  Rayleigh 

Carbon  monoxide 

0.96716 

1.2506 

097  118 

Lord  Rayleigh 

Chlorine 

2.491 

3.1666 

500  593 

Leduc 

Ethane 

1.075 

1.3421 

127  785 

Kolbe 

Ethylene 

0.9852 

1.2520 

097  604 

Saussure 

Hydrogen 

0.06926 

0.09004 

954435 

Regnault 

Hydrogen  sulphide 

1.1895 

1.5230 

182700 

Leduc 

Hydrobromic  acid 

2.71 

3.6163 

558  265 

Lowig 

Hydrochloric  acid 

1.2692 

1.6283 

211  734 

Leduc 

Hydriodic  acid 

4.3757 

5.7106 

756  682 

Thomson 

Methane 

0.5576 

0.7160 

854  913 

Thomson 

Methyl  ether 

1.617 

2.0567 

313171 

Dumas  and  Peligot 

Nitrogen 

0.96737 

1.2542 

098  367 

Lord  Rayleigh 

Nitrogen  dioxide 

1.0372 

1.3417 

127  655 

Leduc 

Nitrogen  monoxide 

1.5301 

1.9688 

294  202 

Leduc 

Oxygen 

1.10535 

1.4292 

155  093 

Lord  Rayleigh 

Sulphur  dioxide 

2.2639 

2.8611 

456  533 

Leduc 

TABLE  XVI 


31 


DENSITY  OF  DRY  ATMOSPHERIC  AIR  AT  760  MM.  PRESSURE  AND 
TEMPERATURES  RANGING  FROM  0°  TO  35° 


Values  of  dt.  rfi0  = 


.0012928    \ 
1  +  .003670 1) 


t 

dt,  760 

log 

t 

dt,  760 

log 

t 

dt,  760 

log 

0.0 

0.0  012  928 

111531 

4.0 

0.0012741 

105  204' 

8.0 

0.0012559 

098  955 

0.1 

12923 

1363 

4.1 

12736 

5033 

8.1 

12  555 

8817 

0.2 

12919 

1229 

4.2 

12732 

4897 

8.2 

12550 

8644 

0.3 

12914 

1061 

4.3 

12728 

4760 

8.3 

12  546 

8505 

0.4 

12909 

0893 

4.4 

12723 

4590 

8.4 

12541 

8332 

0.5 

12904 

0724 

4.5 

12  718 

4419 

8.5 

12537 

8194 

0.6 

12900 

0590 

4.6 

12713 

4248 

8.6 

12532 

8020 

0.7 

12895 

0421 

4.7 

12709 

4111 

8.7 

12528 

7882 

0.8 

12890 

0253 

4.8 

12704 

3941 

8.8 

12524 

7743 

0.9 

12885 

110084 

4.9 

12700 

3804 

8.9 

12519 

7570 

1.0 

0.0  012  SSI 

109  950 

5.0 

0.0012695 

103  633 

9.0 

0.0012515 

097431 

1.1 

12876 

9781 

5.1 

12690 

3462 

9.1 

12511 

7292 

1.2 

12871 

9612 

5.2 

12686 

3325 

9.2 

12506 

7118 

1.3 

12867 

9477 

5.3 

12681 

3154 

9.3 

12501 

6945 

1.4 

12862 

9309 

5.4 

12677 

3017 

9.4 

12497 

6806 

1.5 

12857 

9140 

5.5 

12672 

2845 

9.5 

12492 

6632 

1.6 

12853 

9005 

5.6 

12  668 

2708 

9.6 

12488 

6493 

1.7 

12848 

8  836 

5.7 

12663 

2537 

9.7 

12484 

6354 

1.8 

12843 

S667 

5.8 

12659 

2399 

9.8 

12479 

6180 

1.9 

12  838 

8497 

5.9 

12654 

2228 

9.9 

12475 

6041 

2.0 

0.0012834 

108  362 

6.0 

0.0  012  649 

102  056 

10.0 

0.0012470 

095867 

2.1 

12829 

8193 

6.1 

12645 

1919 

10.1 

12466 

5727 

2.2 

12824 

S024 

6.2 

12640 

1747 

10.2 

12462 

5588 

2.3 

12820 

7888 

6.3 

12636 

1610 

10.3 

12457 

5414 

2.4 

12815 

7719 

6.4 

12631 

1438 

10.4 

12453 

5274 

2.5 

12  810. 

7549 

6.5 

12627 

1300 

10.5 

12448 

5  100 

2.6 

12806 

7414 

6.6 

12622 

1  128 

10.6 

12444 

4960 

2.7 

12801 

7244 

6.7 

12618 

0991 

10.7 

12440 

4820 

2.8 

12797 

7108 

6.8 

12613 

0818 

10.8 

12435 

4646 

2.9 

12792 

6939 

6.9 

12609 

0681 

10.9 

12431 

4506 

3.0 

0.0  012  787 

106  769 

7.0 

0.0012604 

100  508 

11.0 

0.0  012  426 

094331 

3.1 

12783 

6633 

7.1 

12600 

0371 

11.1 

12422 

4192 

3.2 

12778 

6463 

7.2 

12595 

0198 

11.2 

12418 

4052 

3.3 

12773 

6293 

7.3 

12591 

100060 

11.3 

12413 

3877 

3.4 

12769 

6157 

7.4 

12586 

099  888 

11.4 

12409 

3737 

3.5 

12764 

5987 

7.5 

12582 

9750 

11.5 

12404 

3562 

3.6 

12759 

5817 

7.6 

12577 

9577 

11.6 

12400 

3422- 

3.7 

12755 

5681 

7.7 

12573 

9439 

11.7 

12396 

3282 

3.8 

12750 

5510 

7.8 

12  568 

9266 

11.8 

12391 

3106 

3.9 

12746 

5374 

7.9 

12564 

9128 

11.9 

12387 

2966 

32 


TABLE  XVI  (CONTINUED) 


t 

dt,  760 

log 

t 

dt,  760 

log 

t 

dt>  760 

log 

12.0 

0.0012383 

092  826 

16.0 

0.0012211 

086751 

20.0 

0.0012044 

080  770 

12.1 

12378 

2651 

16.1 

12207 

6609 

20.1 

12040 

0627 

12.2 

12374 

2510 

16.2 

12203 

6467 

20.2 

12036 

0482 

12.3 

12370 

2370 

16.3 

12198 

6289 

20.3 

12032 

0338 

12.4 

12365 

2194 

16.4 

12194 

6146 

20.4 

12028 

0193 

12.5 

12361 

2054 

16.5 

12190 

6004 

20.5 

12023 

080  013 

12.6 

12357 

1913 

16.6 

12186 

5861 

20.6 

12019 

079  868 

12.7 

12352 

1737 

16.7 

12181 

5683 

20.7 

12015 

9724 

12.8 

12348 

1597 

16.8 

12177 

5540 

20.8 

12011 

9579 

12.9 

12344 

1456 

16.9 

12173 

5398 

20.9 

12007 

9435 

13.0 

0.0  012  339 

091  280 

17.0 

0.0012169 

085  255 

21.0 

0.0  012  003 

079  290 

13.1 

12335 

1139 

17.1 

12  165 

5112 

21.1 

11999 

9145 

13.2 

12331 

0998 

17.2 

12160 

4934 

21.2 

11995 

9000 

13.3 

12326 

0822 

17.3 

12156 

4791 

21.3 

11991 

8855 

13.4 

12322 

0681 

17.4 

12152 

4648 

21.4 

11987 

8711 

13.5 

12318 

0540 

17.5 

12148 

4505 

21.5 

11982 

8529 

13.6 

12313 

0364 

17.6 

12144 

4362 

21.6 

11978 

8384 

13.7 

12309 

0223 

17.7 

12139 

4183 

21.7 

11974 

8239 

13.8 

12305 

090  082 

17.8 

12135 

4040 

21.8 

11970 

8094 

13.9 

12301 

089  940 

17.9 

12131 

3897 

21.9 

11966 

7949 

14.0 

0.0  012  296 

089  764 

18.0 

0.0012127 

083  753 

22.0 

0.0011  962 

077  804 

14.1 

12292 

9623 

181 

12123 

3610 

22.1 

11958 

7659 

14.2 

12288 

9481 

18.2 

12119 

3467 

22.2 

11954 

7513 

14.3 

12283 

9305 

18.3 

12114 

3288 

22.3 

11950 

7368 

14.4 

12279 

9163 

18.4 

12110 

3144 

22.4 

11  946 

7223 

14.5 

12275 

9022 

18.5 

12  106 

3001 

22.5 

11942 

7077 

14.6 

12270 

8845 

18.6 

12102 

2857 

22.6 

11938 

6932 

14.7 

12266 

8703 

18.7 

12098 

2714 

22.7 

11934 

6786 

14.8 

12262 

8561 

18.8 

12094 

2570 

22.8 

11930 

6640 

14.9 

12258 

8420 

18.9 

12089 

2390 

22.9 

11926 

6495 

15.0 

0.0012253 

088  242 

19.0 

0.0012085 

082  247 

23.0 

0.0011922 

076  349 

15.1 

12249 

8101 

19.1 

12081 

2103 

23.1 

11918 

6203 

15.2 

12  245 

7959 

19.2 

12077 

1959 

23.2 

11914 

6058 

15.3 

12241 

7817 

19.3 

12073 

1815 

23.3 

11  910 

5912 

15.4 

12236 

7640 

19.4 

12069 

1671 

23.4 

11906 

5766 

15.5 

12232 

7498 

19.5 

12065 

1527 

23.5 

11902 

5620 

15.6 

12228 

7355 

19.6 

12060 

1347 

23.6 

11898 

5474 

15.7 

12224 

7213 

19.7 

12  056 

1  203 

23.7 

11894 

5328 

15.8 

12219 

7036 

19.8 

12052 

1059 

23.8 

11889 

5  145 

15.9 

12215 

6894 

19.9 

12048 

0915 

23.9 

11885 

4999 

TABLE  XVI  (CONTINUED) 


33 


t 

dt,  760 

log 

t 

<*t,  760                  lOg 

t 

dt,  760 

log 

24.0 

0.0011881 

074  853 

28.0 

0.0011  723 

069  039 

32.0 

0.0011569 

063  296 

24.1 

11877 

4707 

28.1 

11  719 

8891 

32.1 

11  566 

3183 

24.2 

11873 

4  561 

28.2 

11  716 

8779 

32.2 

11562 

3033 

24.3 

11  869 

4414 

28.3 

11712 

8631 

32.3 

11558 

2883 

24.4 

11865 

4268 

28.4 

11708 

8483 

32.4 

11554 

2732 

24.5 

11861 

4121 

28.5 

11  704 

8334 

32.5 

11550 

2582 

24.6 

11857 

3975 

28.6 

11700 

8186 

32.6 

11547 

2469 

24.7 

11853 

3828 

28.7 

11696 

8037 

32.7 

11  543 

2319 

24.8 

11849 

3682 

28.8 

11692 

7889 

32.8 

11539 

2168 

24.9 

11846 

3572 

28.9 

11688 

7740 

32.9 

11535 

2018 

25.0 

0.0011842 

073  425 

29.0 

0.0011684 

067  592 

33.0 

0.0011531 

061  867 

25.1 

11838 

3278 

29.1 

11681 

7480 

33.1 

11528 

1  754 

25.2 

11834 

3132 

29.2 

11677 

7331 

33.2 

11524 

1603 

25.3 

11830 

2985 

29.3 

11673 

7183 

33.3 

11520 

1453 

25.4 

11826 

2838 

29.4 

11  669 

7034 

33.4 

11516 

1302 

25.5 

11822 

2691 

29.5 

11  665 

6885 

33.5 

11513 

1  189 

25.6 

11818 

2544 

29.6 

11661 

6736 

33.6 

11509 

1038 

25.7 

11814 

2397 

29.7 

11657 

6587 

33.7 

11505 

0887 

25.8 

11810 

2250 

29.8 

11654 

6475 

33.8 

11501 

0736 

25.9 

11806 

2103 

29.9 

11650 

6326 

33.9 

11497 

0585 

26.0 

0.0011802 

071  956 

30.0 

0.0011646 

066177 

34.0 

0.0011494 

060471 

26.1 

11  798 

1808 

30.1 

11642 

6028 

34.1 

11490 

0320 

26.2 

11794 

1661 

30.2 

11638 

5878 

34.2 

11486 

0169 

26.3 

11790 

1514 

30.3 

11634 

5729 

34.3 

11483 

060055 

26.4 

11786 

1366 

30.4 

11630 

5580 

34.4 

11479 

059  904 

26.5 

11782 

1219 

30.5 

11627 

5468 

34.5 

11475 

9753 

26.6 

11778 

1072 

30.6 

11  623 

5318 

34.6 

11471 

9601 

26.7 

11  774 

0924 

30.7 

11619 

5  169 

34.7 

11468 

9488 

26.8 

11  770 

0777 

30.8 

11615 

5019 

34.8 

11464 

9336 

26.9 

11  768 

0703 

30.9 

11611 

4870 

34.9 

11460 

9185 

27.0 

0.0011762 

070  481 

31.0 

0.0011607 

064720 

35.0 

0.0011456 

059033 

27.1 

11  759 

0370 

31.1 

11  603 

4570 

27.2 

11  755 

0223 

31.2 

11600 

4458 

27.3 

11751 

070075 

31.3 

11  596 

4308 

27.4 

11747 

069  927 

31.4 

11592 

4158 

27.5 

11743 

9779 

31.5 

11588 

4009 

27.6 

11739 

9631 

31.6 

11  585 

3896 

27.7 

11  735 

9483 

31.7 

11  581 

3746 

27.8 

11  731 

9  335 

31.8 

11  577 

3596 

27.9 

11727 

9187 

31.9 

11  573 

3446 

34 


TABLE  XVII 


(Ostwald-Luther.   Physiko-chemische  Messungen) 


Degrees 
C. 

Apparent 
weight  of  a  cc. 
of  water 

log 

Volume  of  an 
apparent  gram 
of  water 

log 

10 

.9986 

999392 

1.0014 

.000  608 

11 

85 

9348 

15 

0651 

12 

84 

9305 

16 

0694 

13 

83 

9261 

17 

0738 

14 

82 

9218 

18 

0781 

15 

81 

9174 

19 

0824 

16 

79 

9087 

21 

0911 

17 

77 

9000 

23 

0998 

18 

76 

8956 

24 

1041 

19 

74 

8869 

26 

1  128 

20 

72 

8782 

28 

1214 

21 

70 

8695 

30 

1301 

22 

67 

8565 

33 

1431 

23 

65 

8477 

35 

1517 

24 

63 

8390 

37 

1604 

25 

60 

8259 

40 

1734 

TABLE  XVIII 


35 


SPECIFIC  VOLUME   OF  WATER 

(Thiesen,  Scheel,  and  Diesselhorst,  Wiss.  Abh.  d.  Phys.  Techn.  Reichsanst.  3,  69) 

Hydrogen  Scale 


Tenth  Degrees 

Degrees 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

0 

1.000132 

126 

119 

113 

107 

101 

095 

089 

084 

079 

1 

073 

069 

064 

059 

055 

051 

047 

043 

039 

035 

2 

032 

029 

026 

023 

020 

018 

016 

013 

Oil 

009 

3 

008 

006 

005 

004 

003 

002 

001 

001 

000 

000 

4 

000 

000 

000 

001 

001 

002 

003 

004 

005 

007 

5 

008 

010 

012 

014 

016 

018 

021 

023 

026 

029 

6 

032 

035 

039 

042 

046 

050 

054 

058 

062 

066 

7 

071 

075 

080 

085 

090 

096 

101 

107 

112 

118 

8 

124 

130 

137 

143 

149 

156 

163 

170 

177 

184 

9 

192 

199 

207 

215 

223 

231 

239 

247 

256 

264 

10 

273 

282 

291 

300 

309 

319 

328 

338 

348 

358 

11 

368 

378 

388 

399 

409 

420 

431 

442 

453 

464 

12 

476 

487 

499 

511 

522 

534 

547 

559 

571 

584 

13 

596 

609 

622 

635 

648 

661 

675 

688 

702 

715 

14 

729 

743 

757 

772 

786 

800 

815 

830 

844 

859 

15 

874 

890 

905 

920 

936 

951 

967 

983 

999 

*015 

16 

1.001  031 

048 

064 

081 

098 

114 

131 

148 

165 

183 

17 

200 

218 

235 

253 

271 

289 

307 

325 

343 

361 

18 

380 

399 

417 

436 

455 

474 

493 

513 

532 

.  551 

19 

571 

591 

610 

630 

650 

671 

691 

711 

732 

752 

20 

773 

794 

815 

836 

857 

878 

899 

921 

942 

964 

21 

985 

*007 

*029 

*051 

*073 

*0% 

*118 

*140 

*163 

*186 

22 

1.002  208 

231 

254 

277 

300 

324 

347 

370 

394 

418 

23 

441 

465 

489 

513 

538 

562 

586 

611 

635 

660 

24 

685 

710 

735 

760 

785 

810 

835 

861 

886 

912 

25 

938 

964 

990 

*016 

*042 

*068 

*094 

*121 

*147 

#174 

26 

1.003  201 

227 

254 

281 

308 

336 

363 

390 

418 

445 

27 

473 

501 

529 

556 

585 

613 

641 

669 

698 

726 

28 

755 

783 

812 

841 

870 

899 

928 

957 

987 

*016 

29 

1.004046 

075 

105 

135 

165 

194 

225 

255 

285 

315 

30 

346 

376 

407 

437 

468 

499 

530 

561 

592 

623 

31 

655 

686 

717 

749 

781 

812 

844 

876 

908 

940 

32 

972 

*005 

*037 

*070 

*102 

*135 

*167 

*200 

*233 

*266 

33 

1.005  299 

332 

365 

399 

432 

465 

499 

533 

566 

600 

34 

634 

668 

702 

736 

771 

805 

839 

874 

908 

943 

35 

978 

*013 

*047 

*OS2 

*118 

*153 

*188 

*223 

*259 

#294 

36 


TABLE  XIX 


DENSITY  OF  WATER 

(Thiesen,  Scheel,  and  Diesselhorst,  Wiss.  Abh.  d.  Phys.  Techn.  Reichsanst.  3, 

Hydrogen  Scale 


Tenth  Degrees 

Degrees 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

0 

0.999  868 

874 

881 

887 

893 

899 

905 

911 

916 

922 

1 

927 

932 

936 

941 

945 

950 

954 

957 

961 

965 

2 

968 

971 

974 

977 

980 

982 

985 

987 

989 

991 

3 

992 

994 

995 

996 

997 

998 

999 

999 

*000 

*000 

4 

1.000000 

000 

000 

*999 

*999 

*998 

*997 

*996 

*995 

*993 

5 

0.999  992 

990 

988 

986 

984 

982 

979 

977 

974 

971 

6 

968 

965 

962 

958 

954 

951 

947 

943 

938 

934 

7 

929 

925 

920 

915 

910 

904 

899 

893 

888 

882 

8 

876 

870 

864 

857 

851 

844 

837 

830 

823 

816 

9 

808 

801 

793 

785 

778 

769 

761 

753 

744 

736 

10 

727 

718 

709 

700 

691 

681 

672 

662 

652 

642 

11 

632 

622 

612 

601 

591 

580 

569 

558 

547 

536 

12 

525 

513 

502 

490 

478 

466 

454 

442 

429 

417 

13 

404 

391 

379 

366 

353 

339 

326 

312 

299 

285 

14 

271 

257 

243 

229 

215 

200 

186 

171 

156 

141 

15 

126 

111 

096 

081 

065 

050 

034 

018 

002 

*986 

16 

0.998  970 

953 

937 

920 

904 

887 

870 

853 

836 

819 

17 

801 

784 

766 

749 

731 

713 

695 

677 

659 

640 

18 

622 

603 

585 

566 

547 

528 

509 

490 

471 

451 

19 

432 

412 

392 

372 

352 

332 

312 

292 

271 

251 

20 

230 

210 

189 

168 

147 

126 

105 

083 

062 

040 

21 

019 

*997 

*975 

*953 

*931 

*909 

*887 

*S64 

*S42 

*819 

22 

0.997  797 

774 

751 

728 

705 

682 

659 

635 

612 

588 

23 

565 

541 

517 

493 

469 

445 

421 

396 

372 

347 

24 

323 

298 

273 

248 

223 

198 

173 

147 

122 

096 

25 

071 

045 

019 

*994 

*968 

*941 

*915 

*SS9 

*S63 

*836 

26 

0.996  810 

783 

756 

730 

703 

676 

648 

621 

594 

567 

27 

539 

512 

484 

456 

428 

400 

372 

344 

316 

288 

28 

259 

231 

202 

174 

145 

116 

087 

058 

029 

000 

29 

0.995  971 

941 

912 

882 

853 

823 

793 

763 

733 

703 

30 

673 

643 

613 

582 

552 

521 

491 

460 

429 

398 

31 

367 

336 

305 

273 

242 

211 

179 

148 

116 

084 

32 

052 

020 

*988 

*956 

*924 

*892 

*859 

*S27 

*794 

*762 

33 

0.994  729 

696 

663 

630 

597 

564 

531 

498 

464 

431 

34 

398 

364 

330 

296 

263 

229 

195 

161 

126 

092 

35 

058 

023 

*989 

*954 

*920 

*885 

*850 

*815 

*7SO 

*745 

TABLE  XX 


37 


THE  PROPORTION  BY  WEIGHT  OF 

THE  PROPORTION  BY  VOLUME  OF 

ABSOLUTE  ALCOHOL  IN  100  PARTS 

ABSOLUTE  ALCOHOL  IN  100   VOL- 

OF SPIRITS  OF  DIFFERENT  SPE- 

UMES OF  SPIRITS  OF  DIFFERENT 

CIFIC   GRAVITIES  (Fownes) 

SPECIFIC  GRAVITIES  (Gay-Lussac) 

100 

100 

100 

vol. 

vol. 

vol. 

Per 

cent 

Per 

cent 

Per 

cent 

spirits 

spirits 

spirits 

Sp.  G. 
at  15.5° 

of 
real 
alco- 

Sp. G. 
at  15.5° 

of 
real 
alco- 

Sp. G. 
at  15.5° 

of 

real 
alco- 

Sp. G. 

at  15° 

con- 
tain 
vol.  of 
real 

Sp.  G. 
at  15° 

con- 
tain 
vol.  of 
real 

Sp.  G. 
at  15° 

con- 
tain 
vol.  of 
real 

hol 

hol 

hol 

alco- 

alco- 

alco- 

hol 

hol 

hol 

.9991 

0.5 

.9511 

34 

.8769 

68 

.9985 

1 

.9594 

35 

.8932 

69 

.9981 

1 

.9490 

35 

.8745 

69 

.9970 

2 

.9581 

36 

.8907 

70 

.9965 

2 

.9470 

36 

.8721 

70 

.9956 

3 

.9567 

37 

.8882 

71 

.9947 

3 

.9452 

37 

.8696 

71 

.9942 

4 

.9553 

38 

.8857 

72 

.9930 

4 

.9434 

38 

.8672 

72 

.9929 

5 

.9538 

39 

.8831 

73 

.9914 

5 

.9416 

39 

.8649 

73 

.9916 

6 

.9523 

40 

.8805 

74 

.9898 

6 

.9396 

40 

.8625 

74 

.9903 

7 

.9507 

41 

.8779 

75 

.9884 

7 

.9376 

41 

.8603 

75 

.9891 

8 

.9491 

42 

.8753 

76 

.9869 

8 

.9356 

42 

.8581 

76 

.9878 

9 

.9474 

43 

.8726 

77 

.9855 

9 

.9335 

43 

.8557 

77 

.9867 

10 

.9457 

44 

.8699 

78 

.9841 

10 

.9314 

44 

.8833 

78 

.9855 

11 

.9440 

45 

.8672 

79 

.9828 

11 

.9292 

45 

.8508 

79 

.9844 

12 

.9422 

46 

.8645 

80 

.9815 

12 

.9270 

46 

.8483 

80 

.9833 

13 

.9404 

47 

.8617 

81 

.9802 

13 

.9249 

47 

.8459 

81 

.9822 

14 

.9386 

48 

.8589 

82 

.9789 

14 

.9228 

48 

.8434 

82 

.9812 

15 

.9367 

49 

.8560 

83 

.9778 

15 

.9206 

49 

.8408 

83 

.9802 

16 

.9348 

50 

.8531 

84 

.9766 

16 

.9184 

50 

.8382 

84 

.9792 

17 

.9329 

51 

.8502 

85 

.9753 

17 

.9160 

51 

.8357 

85 

.9782 

18 

.9309 

52 

.8472 

86 

.9741 

18 

.9135 

52 

.8331 

86 

.9773 

19 

.9289 

53 

.8442 

87 

.9728 

19 

.9113 

53 

.8305 

87 

.9763 

20 

.9269 

54 

.8411 

88 

.9716 

20 

.9090 

54 

.8279 

88 

.9753 

21 

.9248 

55 

.8379 

89 

.9704 

21 

.9069 

55 

.8254 

89 

.9742 

22 

.9227 

56 

.8346 

90 

.9691 

22 

.9047 

56 

.8228 

90 

.9732 

23 

.9206 

57 

.8312 

91 

.9678 

23 

.9025 

57 

.8199 

91 

.9721 

24 

.9185 

58 

.8278 

92 

.9665 

24 

.9001 

58 

.8172 

92 

.9711 

25 

.9163 

59 

.8242 

93 

.9652 

25 

.8979 

59 

.8145 

93 

.9700 

26 

.9141 

60 

.8206 

94 

.9638 

26 

.8956 

60 

.8118 

94 

.9690 

27 

.9119 

61 

.8168 

95 

.9623 

27 

.8932 

61 

.8089 

95 

.9679 

28 

.9096 

62 

.8128 

96 

.9609 

28 

.8908 

62 

.8061 

96 

.9668 

29 

.9073 

63 

.8086 

97 

.9593 

29 

.8886 

63 

.8031 

97 

.9657 

30 

.9050 

64 

.8042 

98 

.9578 

30 

.8863 

64 

.8001 

98 

.9645 

31 

.9027 

65 

.8006 

99 

.9560 

31 

.8840 

65 

.7969 

99 

.9633 

32 

.9004 

66 

.7947 

100 

.9544 

32 

.8816 

66 

.7938 

100 

.9621 

33 

.8980 

67 

.9528 

33 

.8793 

67 

.9608 

34 

.8956 

68 

38 


TABLE  XXI 


SPECIFIC  GKAVITY  OF  SOLUTIONS  OF  AMMONIUM  HYDROXIDE  AT  15°  C. 

(Lunge  and  Wiernik,  Zeit.  f.  angew.  Chem.,  1889,  181) 


Sp.  G. 

•Mf 

in  vacuo 

Per  cent 
NH3 
grams 

1  liter 
contains 
NH3 
grams 

Sp.  G. 
at"' 

in  vacuo 

Per  cent 
NH3 
grams 

1  liter 
contains 
NH3 
grams 

Sp.  G. 

atr 

in  vacuo 

Per  cent 
NH3 
grams 

1  liter 
contains 
NH3 
grams 

1.000 

.00 

0.0 

0.960 

9.91 

95.1 

0.920 

21.75 

200.1 

0.998 

.45 

4.5 

958 

10.47 

100.3 

918 

22.39 

205.6 

996 

.91 

9.1 

956 

11.03 

105.4 

916 

23.03 

210.9 

994 

1.37 

13.6 

954 

11.60 

110.7 

914 

23.68 

216.3 

992 

1.84 

18.2 

952 

12.17 

115.9 

912 

24.33 

221.9 

990 

2.31 

22.9 

950 

12.74 

121.0 

910 

24.99 

227.4 

988 

2.80 

27.7 

948 

13.31 

126.2 

908 

25.65 

232.9 

986 

3.30 

32.5 

946 

13.88 

131.3 

906 

26.31 

238.3 

984 

3.80 

37.4 

944 

14.46 

136.5 

904 

26.98 

243.9 

982 

4.30 

42.2 

942 

15.04 

141.7 

902 

27.65 

249.4 

980 

4.80 

47.0 

940 

15.63 

146.9 

900 

28.33 

255.0 

978 

5.30 

51.8 

938 

16.22 

152.1 

898 

29.01 

260.5 

976 

5.80 

56.6 

936 

16.82 

157.4 

896 

29.69 

266.0 

974 

6.30 

61.4 

934 

17.42 

162.7 

894 

30.37 

271.5 

972 

6.80 

66.1 

932 

18.03 

168.1 

892 

31.05 

277.0 

970 

7.31 

70.9 

930 

18.64 

173.4 

890 

31.75 

282.6 

968 

7.82 

75.7 

928 

19.25 

178.6 

888 

32.50 

288.6 

966 

8.33 

80.5 

926 

19.87 

184.2 

886 

33.25 

294.6 

964 

8.84 

85.2 

924 

20.49 

189.3 

884 

34.10 

301.4 

962 

9.35 

89.9 

922 

21.12 

194.7 

882 

34.95 

308.3 

TABLE  XXII 
SPECIFIC  GRAVITY  OF  SOLUTIONS  OF  HYDROCHLORIC  ACID  AT  15°  C. 

(Lunge  and  Marchlewski,  Zeit.  angew.  Chem.,  1891,  135) 


Sp.  G. 
atL- 

in  vacuo 

100  pts. 
by  wt. 
contain 
grams 
HC1 

1  liter 
contains 
grams 
HC1 

Sp.  g. 

atr 

in  vacuo 

100  pts. 
by  wt. 
contain 
grams 
HC1 

1  liter 
contains 
grams 
HC1 

Sp.  G. 

.tv 

in  vacuo 

100  pts. 
by  wt. 
contain 
grams 
HC1 

1  liter 
contains 
grams 
HC1 

1.000 

0.16 

1.6 

1.070 

14.17 

152 

1.140 

27.66 

315 

1.005 

1.15 

12.0 

1.075 

15.16 

163 

1.145 

28.61 

328 

1.010 

2.14 

22.0 

1.080 

16.15 

174 

1.150 

29.57 

340 

1.015 

3.12 

32.0 

1.085 

17.13 

186 

1.155 

30.55 

353 

1.020 

4.13 

42.0 

1.090 

18.11 

197 

1.160 

31.52 

366 

1.025 

5.15 

53 

.095 

19.06 

209 

1.165 

32.49 

379 

1.030 

6.15 

64 

.100 

20.01 

220 

1.170 

33.46 

392 

1.035 

7.15 

74 

.105 

20.97 

232 

1.175 

34.42 

404 

1.040 

8.16 

85 

.110 

21.92 

243 

1.180 

35.39  . 

418 

1.045 

9.16 

96 

.115 

22.86 

255 

1.185 

36.31 

430 

1.050 

10.17 

107 

.120 

23.82 

267 

1.190 

37.23 

443 

1.055 

11.18 

118 

.125 

24.78 

278 

1.195 

38.16 

456 

1.060 

12.19 

129 

.130 

25.75 

291 

1.200 

39.11 

469 

1.065 

13.19 

141 

.135 

26.70 

303 

TABLE  XXIII 


39 


CONSTANT  BOILING  SOLUTION  OF  HYDROCHLORIC  ACID 

(Hulett  and  Bonner,  Jour.  Am.  Chem.  Soc.,  31,  390) 


Grams  constant 

Barometric 

Per  cent 

boiling  distillate 

pressure 

HC1 

containing 

1  mol  HC1 

770 

20.218 

180.390 

760 

20.242 

180.170 

750 

20.266 

179.960 

740 

20.290 

179.745 

730 

20.314 

179.530 

The  easiest  and  most  accurate  method  of  preparing  standard  solutions  of 
hydrochloric  acid  is  to  weigh  out  a  definite  amount  of  the  constant  boiling 
solution  of  hydrochloric  acid  and  dilute  this  to  a  certain  volume.  The  con- 
stant boiling  solution  is  obtained  by  diluting  the  concentrated  hydrochloric 
acid  of  the  laboratory  with  an  equal  volume  of  water.  Distill  from  a  retort 
or  distilling  flask  connected  with  a  condenser.  When  three  fourths  has  been 
distilled  off,  change  the  receiver  and  collect  as  much  of  the  remainder 
as  is  desirable.  The  last  fraction  is  the  constant  boiling  solution,  and  if  the 
barometric  pressure  is  noted,  the  exact  weight  of  this  solution  which  when 
diluted  to  a  liter  yields  a  normal  solution  can  be  ascertained  by  reference 
to  the  table. 


40 


TABLE  XXIV 


SPECIFIC  GRAVITY  OF  NITRIC  ACID  AT  15°  C. 
(Lunge  and  Rey,  Zeit.  angew.  Chem.,  1891,  165) 


Specific 
gravity 
at  15° 
in  vacuo 

100  pts. 
by  wt. 
contain 
grams 
HN03 

1  liter 
contains 
grams 
HN03 

Specific 
gravity 
at^°in 
vacuo 

100  pts. 
by  wt. 
contain 
grams 
HN03 

1  liter 
contains 
grams 
HN03 

Specific 
gravity 
at  ^°  in 
vacuo 

100  pts. 
by  wt. 
contain 
grams 
HN03 

1  liter 
contains 
grams 
HN03 

1.000 

0.10 

1 

1.205 

33.09 

399 

1.410 

67.50 

952 

1.005 

1.00 

10 

1.210 

33.82 

409 

1.415 

68.63 

971 

1.010 

1.90 

19 

1.215 

34.55 

420 

1.420 

69.80 

991 

1.015 

2.80 

28 

1.220 

35.28 

430 

1.425 

70.98 

1011 

1.020 

3.70 

38 

1.225 

36.03 

441 

1.430 

72.17 

1032 

1.025 

4.60 

47 

1.230 

36.78 

452 

1.435 

73.39 

1053 

1.030 

5.50 

57 

1.235 

37.53 

463 

1.440 

74.68 

1075 

.035 

6.38 

66 

1.240 

38.29 

475 

1.445 

75.98 

1098 

.040 

7.26 

75 

1.245 

39.05 

486 

1.450 

77.28 

1121 

1.045 

8.13 

85 

1.250 

39.82 

498 

1.455 

78.60 

1144 

.050 

8.99 

94 

1.255 

40.58 

509 

1.460 

79.98 

1168 

.055 

9.84 

104 

1.260 

41.34 

521 

1.465 

81.42 

1193 

1.060 

10.68 

113 

1.265 

42.10 

533 

1.470 

82.90 

1219 

1.065 

11.51 

123 

1.270 

42.87 

544 

1.475 

84.45 

1246 

1.070 

12.33 

132 

1.275 

43.64 

556 

1.480 

86.05 

1274 

1.075 

13.15 

141 

1.280 

44.41 

568 

1.485 

87.70 

1302 

1.080 

13.95 

151 

1.285 

45.18 

581 

1.490 

89.60 

1335 

1.085 

14.74 

160 

1.290 

45.95 

593 

1.495 

91.60 

1369 

1.090 

15.53 

169 

1.295 

46.72 

603 

1.500 

94.09 

1411 

1.095 

16.32 

179 

1.300 

47.49 

617 

1.501 

94.60 

1420 

1.100 

17.11 

188 

1.305 

48.26 

630 

1.502 

95.08 

1428 

1.105 

17.89 

198 

1.310 

49.07 

643 

1.503 

95.55 

1436 

1.110 

18.67 

207 

1.315 

49.89 

656 

1.504 

96.00 

1444 

1.115 

19.45 

217 

1.320 

50.71 

669 

1.505 

96.39 

1451 

1.120 

20.23 

227 

1.325 

51.53 

683 

1.506 

96.76 

1457 

1.125 

21.00 

236 

1.330 

52.37 

697 

1.507 

97.13 

1464 

1.130 

21.77 

246 

1.335 

53.22 

710 

1.508 

97.50 

1470 

1.135 

22.54 

256 

1.340 

54.07 

725 

1.509 

97.84 

1476 

1.140 

23.31 

266 

1.345 

54.93 

739 

1.510 

98.10 

1481 

1.145 

24.08 

276 

1.350 

55.79 

753 

1.511 

98.32 

1486 

1.150 

24.84 

286 

1.355 

56.66 

768 

1.512 

98.53 

1490 

1.155 

25.60 

296 

1.360 

57.57 

783 

1.513 

98.73 

1494 

1.160 

26.36 

306 

.365 

58.48 

798 

1.514 

98.90 

1497 

1.165 

27.12 

316 

.370 

59.39 

814 

1.515 

99.01 

1501 

1.170 

27.88 

326 

.375 

60.30 

829 

1.516 

99.21 

1504 

1.175 

28.63 

336 

.380 

61.27 

846 

1.517 

99.34 

1507 

1.180 

29.38 

347 

.385 

62.24 

862 

1.518 

99.46 

1510 

1.185 

30.13 

357 

.390 

63.23 

879 

1.519 

99.57 

1512 

1.190 

30.88 

367 

1.395 

64.25 

896 

1.520 

99.67 

1515 

1.195 

31.62 

378 

1.400 

65.30 

914 

1.200 

32.36 

388 

1.405 

66.40 

933 

TABLE  XXV 


41 


SPECIFIC  GRAVITY  OF  SULPHURIC  ACID  AT  15°  C. 

(Lunge,  Isler  and  Naef,  Zeit.  angew.  Chem.,  1890,  131) 


Sp.  G. 
at  f  in 
vacuo 

100  pts. 
by  wt. 
contain 
grams 
H2S04 

1  liter 
contains 
grams 
H2S04 

Sp.  G. 

at  ^°  in 
vacuo 

100  pts. 
by  wt. 
contain 
grams 
H2S04 

1  liter 
contains 
grams 
H2S04 

Sp.  G. 

at^°in 
vacuo 

100  pts. 
by  wt. 
contain 
grams 
H2S04 

1  liter 
contains 
grams 
H2S04 

1.000 

.09 

1 

1.225 

30.48 

373 

1.450 

55.03 

798 

1.005 

.83 

8 

1.230 

31.11 

382 

1.455 

55.50 

808 

1.010 

1.57 

16 

1.235 

31.70 

391 

1.460 

55.97 

817 

1.015 

2.30 

23 

1.240 

32.28 

400 

1.465 

56.43 

827 

1.020 

3.03 

31 

1.245 

32.86 

409 

1.470 

56.90 

837 

1.025 

3.76 

39 

1.250 

33.43 

418 

1.475 

57.37 

846 

1.030 

4.49 

46 

1.255 

34.00 

426 

1.480 

57.83 

856 

1.035 

5.23 

54 

1.260 

34.57 

435 

1.485 

58.28 

865 

1.040 

5.96 

62 

1.265 

35.14 

444 

1.490 

58.74 

876 

1.045 

6.67 

71 

1.270 

35.71 

454 

1.495 

59.22 

885 

1.050 

7.37 

77 

1.275 

36.29 

462 

1.500 

59.70 

896 

1.055 

8.07 

85 

1.280 

36.87 

472 

1.505 

60.18 

906 

1.060 

8.77 

93 

1.285 

37.45 

481 

1.510 

60.65 

916 

1.065 

9.47 

102 

1.290 

38.03 

490 

1.515 

61.12 

926 

1.070 

10.19 

109 

1.295 

38.61 

500 

1.520 

61.59 

936 

1.075 

10.90 

117 

1.300 

39.19 

510 

1.525 

62.06 

946 

1.080 

11.60 

125 

1.305 

39.77 

519 

1.530 

62.53 

957 

1.085 

12.30 

133 

1.310 

40.35 

529 

1.535 

63.00 

967 

1.090 

12.99 

142 

1.315 

40.93 

538 

1.540 

63.43 

977 

1.095 

13.67 

150 

1.320 

41.50 

548 

1.545 

63.85 

987 

1.100 

14.35 

158 

1.325 

42.08 

557 

1.550 

64.26 

996 

1.105 

15.03 

166 

1.330 

42.66 

567 

1.555 

64.67 

1006 

1.110 

15.71 

175 

1.335 

43.20 

577 

1.560 

65.08 

1015 

1.115 

16.36 

183 

1.340 

43.74 

586 

1.565 

65.49 

1025 

1.120 

17.01 

191 

1.345 

44.28 

596 

1.570 

65.90 

1035 

1.125 

17.66 

199 

1.350 

44.82 

605 

1.575 

66.30 

1044 

1.130 

18.31 

207 

1.355 

45.35 

614 

1.580 

66.71 

1054 

1.135 

18.96 

215 

1.360 

45.88 

624 

1.585 

67.13 

1064 

1.140 

19.61 

223 

1.365 

46.41 

633 

1.590 

67.59 

1075 

1.145 

20.26 

231 

1.370 

46.94 

643 

1.595 

68.05 

1085 

1.150 

20.91 

239 

1.375 

47.47 

653 

1.600 

68.51 

1096 

1.155 

21.55 

248 

1.380 

48.00 

662 

1.605 

68.97 

1107 

.160 

22.19 

257 

1.385 

48.53 

672 

1.610 

69.43 

1118 

.165 

22.83 

266 

1.390 

49.06 

682 

1.615 

69.89 

1128 

.170 

23.47 

275 

1.395 

49.59 

692 

1.620 

70.32 

1139 

.175 

24.12 

283 

1.400 

50.11 

702 

1.625 

70.74 

1150 

.180 

24.76 

292 

1.405 

50.63 

711 

1.630 

71.16 

1160 

.185 

25.40 

301 

1.410 

51.15 

721 

1.635 

71.57 

1170 

.190 

26.04 

310 

1.415 

51.66 

730 

1.640 

71.99 

1181 

.195 

26.68 

319 

1.420 

52.15 

740 

1.645 

72.40 

1192 

.200 

27.32 

328 

1.425 

52.63 

750 

1.650 

72.82 

1202 

.205 

27.95 

337 

1.430 

53.11 

759 

1.655 

73.23 

1212 

.210 

28.58 

346 

1.435 

53.59 

769 

1.660 

73.64 

1222 

1.215 

29.21 

355 

1.440 

54.07 

779 

1.665 

74.07 

1233 

1.220 

29.84 

364 

1.445 

54.55 

789 

1.670 

74.51 

1244 

TABLE  XXV  (CONTINUED) 

SPECIFIC  GRAVITY  OF  SULFURIC  ACID  AT  15°  C. 

(Lunge,  Isler  and  Naef,  Zeit.  angew.  Chem.,  1890,  131) 


Sp.  G. 

atV5°m 
vacuo 

100  pts. 
by  wt. 
contain 
grams 
H2S04 

1  liter 
contains 
grams 
H2S04 

Sp.  G 

at^in 
vacuo 

100  pts. 
by  wt. 
contain 
grams 
H2S04 

1  liter 
contains 
grams 
H2S04 

Sp.  G. 
at  £°  in 
vacuo 

100  pts. 
bywt. 
contain 
grams 
H2S04 

1  liter 
contains 
grams 
H2S04 

1.675 

74.97 

1256 

1.775 

83.90 

1489 

1.831 

92.30 

1690 

1.680 

75.42 

1267 

1.780 

84.50 

1504 

1.832 

92.52 

1695 

1.685 

75.86 

1278 

1.785 

85.10 

1519 

1.833 

92.75 

1700 

1.690 

76.30 

1289 

1.790 

85.70 

1534 

1.834 

93.05 

1706 

1.695 

76.73 

1301 

1.795 

86.30 

1549 

1.835 

93.43 

1713 

1.700 

77.17 

1312 

1.800 

86.90 

1564 

1.836 

93.80 

1722 

1.705 

77.60 

1323 

1.805 

87.60 

1581 

1.837 

94.20 

1730 

1.710 

78.04 

1334 

1.810 

88.30 

1598 

1.838 

94.60 

1739 

1.715 

78.48 

1346 

1.815 

89.05 

1621 

1.839 

95.00 

1748 

1.720 

78.92 

1357 

1.820 

90.05 

1639 

1.840 

95.60 

1759 

1.725 

79.36 

1369 

1.821 

90.20 

1643 

1.8405 

95.95 

1765 

1.730 

79.80 

1381 

1.822 

90.40 

1647 

1.8410 

97.00 

1786 

1.735 

80.24 

1392 

1.823 

9P.60 

1651 

1.8415 

97.70 

1799 

1.740 

80.68 

1404 

1.824 

90.80 

1656 

1.8410 

98.20 

1808 

1.745 

81.12 

1416 

1.825 

91.00 

1661 

1.8405 

98.70 

1816 

1.750 

81.56 

1427 

1.826 

91.25 

1666 

1.8400 

99.20 

1825 

1.755 

82.00 

1439 

1.827 

91.50 

1671 

1.8395 

99.45 

1830 

1.760 

82.44 

1451 

1.828 

91.70 

1676 

1.8390 

99.70 

1834 

1.765 

82.88 

1463 

1.829 

91.90 

1681 

1.8385 

99.95 

1838 

1.770 

83.32 

1475 

1.830 

92.10 

1685 

TABLE  XXVI A 


43 


CORRECTIONS  FOR  THE  EXPOSED  THREAD  OF  MERCURY  THERMOMETERS 

(Landolt-Bornstein) 
np(T-t) 

n  is  the  length  of  exposed  thread  expressed  in  terms  of  the  thermometer  graduations, 
/3  the  apparent  coefficient  of  expansion  of  mercury  in  glass.  T  the  temperature  read  off, 
t,  the  mean  temperature  of  the  exposed  thread.  For  temperatures  lower  than  100°  /3 
varies  from  ^V  o  to  srW'  depending  on  the  glass,  and  for  higher  temperatures  the 
fraction  is  somewhat  smaller. 

TV  THERMOMETERS,  GRADUATED  FROM  0°  TO  100° 
(Length  of  degrees  about  4  mm.) 


T—  t  = 

30° 

35° 

40° 

45° 

50° 

55° 

60° 

65° 

70° 

75° 

80° 

85° 

n=10° 

.05 

.05 

.05 

.05 

.05 

.05 

.05 

.05 

.1 

.1 

.1 

.1 

20° 

.1 

.1 

.15 

.15 

.15 

.15 

.15 

.20 

.2 

.2 

.2 

.25 

30° 

.2 

.2 

.25 

.25 

.25 

.25 

.25 

.3 

.3 

.35 

.35 

.35 

40° 

.3 

.3 

.3 

.35 

.35 

.35 

.4 

.4 

.45 

.45 

.5 

.5 

50° 

.35 

.4 

.4 

.4 

.45 

.45 

.5 

.5 

.55 

.55 

.6 

.65 

60° 

.45 

.5 

.5 

.55 

.55 

.55 

.6 

.65 

.65 

.7 

.75 

.8 

70° 

.65 

.7 

.7 

.75 

.8 

.85 

.9 

80° 

.75 

.8 

.85 

.95 

1.0 

1.1 

90° 

.9 

1.0 

1.1 

1.1 

1.2 

100° 

1.1 

1.2 

1.3 

1.3 

44 


TABLE  XXVI  B 


THERMOMETERS  GRADUATED  FROM  0°  TO  360° 
(Length  of  degrees  1  to  1.6  mm.) 


T-t  = 

70° 

80° 

90° 

100° 

110° 

120° 

130° 

140° 

150° 

160° 

170° 

180° 

190° 

200° 

210° 

220° 

72  =  10° 

0. 

.05 

.05 

.05 

.1 

.1 

.1 

.15 

.2 

.2 

.2 

.25 

.3 

.35 

.35 

.40 

20° 

.15 

.15 

.2 

.2 

.25 

.3 

.3 

.4 

.45 

.45 

.5 

.55 

.55 

.60 

.65 

.65 

30° 

.25 

.3 

.35 

.4 

.45 

.5 

.55 

.6 

.65 

.7 

.75 

.8 

.85 

.9 

.95 

.95 

40° 

.35 

.4 

.5 

.55 

.6 

.7 

.75 

.8 

.90 

.95 

1.0 

1.0 

1.1 

1.2 

1.2 

1.3 

50° 

.45 

.55 

.6 

.7 

.8 

.9 

.95 

1.0 

1.1 

1.2 

1.2 

1.3 

1.4 

1.4 

1.5 

1.6 

60° 

.55 

.65 

.75 

.9 

1.0 

1.1 

1.2 

1.2 

1.3 

1.4 

1.5 

1.6 

1.7 

1.7 

1.8 

1.9 

70° 

.7 

.8 

.9 

1.1 

1.2 

1.3 

1.4 

1.5 

1.6 

1.7 

1.8 

1.9 

1.9 

2.0 

2.1 

2.2 

80° 

.8 

.9 

1.0 

1.2 

1.4 

1.5 

1.6 

1.7 

1.8 

1.9 

2.0 

2.1 

2.2 

2.3 

2.4 

2.5 

90° 

.9 

1.0 

1.2 

1.4 

1.6 

1.7 

1.9 

2.0 

2.1 

2.2 

2.3 

2.4 

2.5 

2.6 

2.8 

2.9 

100° 

1.0 

1.2 

1.3 

1.6 

1.8 

2.0 

2.1 

2.2 

2.3 

2.4 

2.6 

2.7 

2.8 

2.9 

3.1 

3.2 

110° 

1.8 

2.0 

2.2 

2.3 

2.4 

2.5 

2.7 

2.8 

3.0 

3.1 

3.3 

3.4 

3.6 

120° 

2.0 

2.2 

2.4 

2.6 

2.7 

2.8 

2.9 

3.1 

3.3 

3.4 

3.6 

3.7 

3.9 

130° 

2.4 

2.7 

2.8 

2.9 

3.0 

3.2 

3.4 

3.6 

3.7 

3.9 

4.1 

4.3 

140° 

2.7 

2.9 

3.1 

3.2 

3.3 

3.5 

3.7 

3.9 

4.0 

4.2 

4.4 

4.6 

150° 

3.5 

3.7 

4.0 

4.1 

4.3 

4.6 

4.8 

5.0 

160° 

3.7 

4.0 

4.2 

4.5 

4.7 

4.9 

5.1 

5.4 

170° 

4.0 

4.3 

4.5 

4.8 

5.0 

5.2 

5.5 

5.8 

180° 

4.3 

4.5 

4.8 

5.1 

5.3 

5.6 

5.9 

6.1 

190° 

5.4 

5.6 

5.9 

6.2 

6.5 

200° 

5.7 

6.0 

6.3 

6.6 

6.9 

210° 

6.3 

6.7 

7.0 

7.3 

220° 

6.7 

7.0 

7.4 

7.7 

TABLE  XXVII 
FIXED  POINTS  OF  THE  THERMOMETRIC  SCALE 

(Transition  temperatures) 


H.  Scale 

Na2Cr04  - 

10H20 

-  Na  CrO 

•  6H20 

19.5251 

Na2004. 

lOHtO 

—  Na2Cr04 

•4H20 

19.987  I 

Richards 

and  Kelley 

Na2Cr04  . 

6H90 

-  Na2Cr04 

•4H20 

25.90  J 

Na2C08  - 

10H20 

-  Na2C03 

•  7H20 

32.00  1 

Na2C03  . 

10H20 

-  Na2C03 

-     H20 

32.96    I 

Wells  and  McAdam 

Na2C03  • 

7H00 

-  Na2C03 

•     H20 

35.37   J 

Na2S04  • 
NaBr      . 

10H90 
2H2"0 

-  Na2S04 
-NaBr 

32.3831 
50.674  J 

Richards 

and  Wells 

MnCl2    . 

4H20 

-  MnCl2 

.2H20 

58.089 

Richards 

and  Wrede 

TABLE  XXVIII 


45 


CORRECTIONS  FOR  LOSS  OF  WEIGHT  IN  AIR 

The  following  table,  calculated  by  Kohlrausch,  contains  corrections,  C,  expressed  in 
milligrams,  to  be  added  algebraically  to  each  gram  of  apparent  weight  of  a  substance, 
the  specific  gravity  of  which  is  S. 


S 

C 

S 

C 

S 

C 

0.7 

+  1.57 

2.0 

+  0.458 

9 

-0.009 

0.8 

+  1.36 

2.5 

+  0.337 

10 

-  0.023 

0.9 

+  1.19 

3.0 

+  0.257 

11 

-  0.034 

1.0 

+  1.06 

3.5 

+  0.200 

12 

-  0.043 

1.1 

+  0.95 

4.0 

+  0.157 

13 

-  0.050 

1.2 

+  0.86 

4.5 

+  0.142 

14 

-  0.057 

1.3 

+  0.78 

5.0 

+  0.097 

15 

-  0.063 

1.4 

+  0.71 

5.5 

+  0.075 

16 

-  0.068 

1.5 

+  0.66 

6.0 

+  0.057 

17 

-  0.072 

1.6 

+  0.61 

6.5 

+  0.042 

IS 

-  0.076 

1.7 

+  0.56 

7-0 

+  0.029 

19 

-  0.080 

1.8 

+  0.52 

7.5 

+  0.017 

20 

-  0.083 

1.9 

+  0.49 

8.0 

+  0.007 

The  following  values  are  of  constant  use  in  revising  the  atomic  weights  of  the  elements 
by  means  of  their  halides. 

Vacuum  correction  per 
apparent  gram 

Ag  _  0.000031  gram 

AgBr  +  0.000041  gram 

AgCl  +0.000075  gram 

Agl  +  0.000071  gram 


Brass  weights 
Glass 


Specific 
gravity 

8.3 
2.5 


Vacuum  correction 
per  apparent  gram. 

-  0.000145 
+  0.000335 


TABLE  XXIX 

LOGARITHMS  OF  NUMBERS 
(From  1  to  10,000) 


N. 

log 

N. 

log 

N. 

log 

N. 

log 

1 

0.000000 

26 

1.414973 

51 

1.707570 

76 

1.880814 

2 

0.301030 

27 

1.431364 

52 

1.716003 

77 

1.886491 

3 

0.477121 

28 

1.447158 

53 

1.724276 

78 

,  1.892095 

4 

0.602060 

29 

1.462398 

54 

1.732394 

79 

1.897627 

5 

0.698970 

30 

1.477121 

55 

1.740363 

80 

1.903090 

6 

0.778151 

31 

1.491362 

56 

1.748188 

81 

1.908485 

7 

0.845098 

32 

1.505150 

57 

1.755875 

82 

1.913814 

8 

0.903090 

33 

1.518514 

58 

1.763428 

83 

1.919078 

9 

•0.954243 

34 

1.531479 

59 

1.770852 

84 

1.924279 

10 

1.000000 

35 

1.544068 

60 

1.778151 

85 

1.929419 

11 

1.041393 

36 

1.556303 

61 

1.785330 

86 

1.934498 

12 

1.079181 

37 

1.568202 

6? 

1.792392 

87 

1.939519 

13 

1.113943 

38 

1.579784 

63 

1.799341 

88 

1.944483 

14 

1.146128 

39 

1.591065 

64 

1.806181 

89 

1.949390 

15 

1.176091 

40 

1.602060 

65 

1.812913 

90 

1.954243 

16 

1.204120 

41 

1.612784 

66 

1.819544 

91 

1.959041 

17 

1.230449 

42 

1.623249 

67 

1.826075 

92 

1.963788 

18 

1.255273 

43 

1.633468 

68 

1.832509 

93 

1.968483 

19 

1.278754 

44 

1.643453 

69 

1.838849 

94 

1.973128 

20 

1.301030 

..  45 

1.653213 

70 

1.845098 

95 

1.977724 

21 

1.322219 

46 

1.662758 

71 

1.851258 

96 

1.982271 

22 

1.342423 

47 

1.67209S 

72 

1.857333 

97 

1.986772 

23 

1.361728 

48 

1.681241 

73 

1.863323 

98 

1.991226 

24 

1.380211 

49 

1.690196 

74 

1.869232 

99 

1.995635 

25 

1.397940 

50 

1.698970 

75 

1.875061 

100 

2.000000 

REMARK.  In  the  following  table,  in  the  nine  right-hand  columns  of  each 
page,  where  the  first  or  leading'  figures  change  from  9's  to  O's,  asterisks  are 
introduced  instead  of  the  O's,  to  catch  the  eye,  and  to  indicate  that  from 
thence  the  two  figures  of  the  logarithm  to  be  taken  from  the  second  column 
stand  in  the  next  line  below. 


TABLE  XXIX  (CONTINUED) 


4T 


N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

D. 

100 

000000 

0434 

0868 

1301 

1734 

2166 

2598 

3029 

3461 

3891 

432 

101 

4321 

4751 

5181 

5609 

6038 

6466 

6894 

7321 

7748 

8174 

428 

102 

8600 

9026 

9451 

9876 

*300 

*724 

1147 

1570 

1993 

2415 

424 

103 

012837 

3259 

3680 

4100 

4521 

4940 

5360 

5779 

6197 

6616 

419 

104 

7033 

7451 

7868 

8284 

8700 

9116 

9532 

9947 

*361 

*775 

416 

105 

021189 

1603 

2016 

2428 

2841 

3252 

3664 

4075 

4486 

4896 

412 

106 

5306 

5715 

6125 

6533 

6942 

7350 

7757 

8164 

8571 

8978 

408 

107 

9384 

9789 

*195 

*600 

1004 

1408 

1812 

2216 

2619 

3021 

404 

108 

033424 

3826 

4227 

4628 

5029 

5430 

5830 

6230 

6629 

7028 

400 

109 

7426 

7825 

8223 

8620 

9017 

9414 

9811 

*207 

*602 

*998 

396 

110 

041393 

1787 

2182 

2576 

2969 

3362 

3755 

4148 

4540 

4932 

393 

111 

5323 

5714 

6105 

6495 

6885 

7275 

7664 

8053 

8442 

8830 

389 

112 

9218 

9606 

9993 

*380 

*766 

1153 

1538 

1924 

2309 

2694 

386 

113 

053078 

3463 

3846 

4230 

4613 

4996 

5378 

5760 

6142 

6524 

382 

114 

6905 

7286 

7666 

8046 

8426 

8805 

9185 

9563 

9942 

*320 

379 

115 

060698 

1075 

1452 

1829 

2206 

2582 

2958 

3333 

3709 

4083 

376 

116 

4458 

4832 

5206 

5580 

5953 

6326 

6699 

7071 

7443 

7815 

372 

117 

8186 

8557 

8928 

9298 

9668 

**3S 

*407 

*776 

1145 

1514 

369 

118 

071SS2 

2250 

2617 

2985 

3352 

3718 

4085 

4451 

4816 

5182 

366 

119 

5547 

5912 

6276 

6640 

7004 

7368 

7731 

8094 

8457 

8819 

363 

120 

079181 

9543 

9904 

*266 

*626 

*987 

1347 

1707 

2067 

2426 

360 

121 

082785 

3144 

3503 

3861 

4219 

4576 

4934 

5291 

5647 

6004 

357 

122 

6360 

6716 

7071 

7426 

7781 

8136 

8490 

8845 

9198 

9552 

355 

123 

9905 

*258 

*611 

*963 

1315 

1667 

2018 

2370 

2721 

3071 

351 

124 

093422 

3772 

4122 

4471 

4820 

5169 

5518 

5866 

6215 

6562 

349 

125 

6910 

7257 

7604 

7951 

8298 

8644 

8990 

9335 

9681 

**26 

346 

126 

100371 

0715 

1059 

1403 

1747 

2091 

2434 

2777 

3119 

3462 

343 

127 

3804 

4146 

4487 

4828 

5169 

5510 

5851 

6191 

6531 

6871 

340 

128 

7210 

7549 

7888 

8227 

8565 

8903 

9241 

9579 

9916 

*253 

.338 

129 

110590 

0926 

1263 

1599 

1934 

2270 

2605 

2940 

3275 

3609 

335 

130 

113943 

4277 

4611 

4944 

5278 

5611 

5943 

6276 

6608 

6940 

333 

131 

7271 

7603 

7934 

8265 

8595 

8926 

9256 

9586 

9915- 

*245 

330 

132 

120574 

0903 

1231 

1560 

1888 

2216 

2544 

2871 

3198 

3525 

328 

133 

3852 

4178 

4504 

4830 

5156 

5481 

5806 

6131 

6456 

6781 

325 

134 

7105 

7429 

7753 

8076 

8399 

8722 

9045 

0268 

9690 

**12 

323 

135 

130334 

0655 

0977 

1298 

1619 

1939 

2260 

*SO 

2900 

3219 

321 

136 

3539 

3858 

4177 

4496 

4814 

5133 

5451 

5769 

6086 

6403 

318 

137 

6721 

7037 

7354 

7671 

7987 

8303 

8618 

8934 

9249 

9564 

315 

138 

9879 

*194 

*508 

*S22 

1'136 

1450 

1763 

2076 

2389 

2702 

314 

139 

143015 

3327 

3639 

3951 

4263 

4574 

4885 

5196 

5507 

5818 

311 

140 

146128 

6438 

6748 

7058 

7367 

7676 

7985 

8294 

8603 

8911 

309 

141 

9219 

9527 

9835 

*142 

*449 

*756 

1063 

1370 

1676 

1982 

307 

142 

152288 

2594 

2900 

3205 

3510 

3815 

4120 

4424 

4728 

5032 

305 

143 

5336 

5640 

5943 

6246 

6549 

6852 

7154 

7457 

7759 

8061 

303 

144 

8362 

8664 

8965 

9266 

9567 

9868 

*168 

*469 

*769 

1068 

301 

145 

161368 

1667 

1967 

2266 

2564 

2863 

3161 

3460 

3758 

4055 

299 

146 

4353 

4650 

4947 

5244 

5541 

5838 

6134 

6430 

6726 

7022 

297 

147 

7317 

7613 

7908 

8203 

8497 

8792 

9086 

9380 

9674 

9968 

295 

148 

170262 

0555 

0848 

1141 

1434 

1726 

2019 

2311. 

2603 

2895 

293 

149 

3186 

3478 

3769 

4060 

-4351 

4641 

4932 

5222 

5512 

5802 

291 

N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

D. 

48 


TABLE  XXIX  (CONTINUED) 


N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

D. 

150 

176091 

6381 

6670 

6959 

7248 

7536 

7825 

8113 

8401 

8689 

289 

151 

8977 

9264 

9552 

9839 

*126 

*413 

*699 

*9SS 

1272 

1558 

287 

152 

181844 

2129 

2415 

2700 

2985 

3270 

3555 

3839 

4123 

4407 

285 

153 

4691 

4975 

5259 

5542 

5825 

6108 

6391 

6674 

6956 

7239 

283 

154 

7521 

7803 

80S4 

8366 

8647 

8928 

9209 

9490 

9771 

**51 

281 

155 

190332 

0612 

0892 

1171 

1451 

1730 

2010 

22S9 

2567 

2846 

279 

156 

3125 

3403 

3681 

3959 

4237 

4514 

4792 

5069 

5346 

5623 

278 

157 

5899 

6176 

6453 

6729 

7005 

7281 

7556 

7832 

8107 

8382 

276 

158 

8657 

8932 

9206 

9481 

9755 

**29 

*303 

*577 

*S50 

1124 

274 

159 

201397 

1670 

1943 

2216 

2488 

2761 

3033 

3305 

3577 

3848 

272 

160 

204120 

4391 

4663 

4934 

5204 

5475 

5746 

6016 

6286 

6556 

271 

161 

6826 

7096 

7365 

7634 

7904 

8173 

8441 

8710 

8979 

9247 

269 

162 

9515 

9783 

**51 

*319 

*5S6 

*S53 

1121 

13S8 

1654 

1921 

267 

163 

2121S8 

2454 

2720 

2986 

3252 

3518 

3783 

4049 

4314 

4579 

266 

164 

4844 

5109 

5373 

5638 

5902 

6166 

6430 

6694 

6957 

7221 

264 

165 

7484 

7747 

8010 

8273 

8536 

8798 

9060 

9323 

9585 

9846 

262 

166 

220108 

0370 

0631 

0892 

1153 

1414 

1675 

1936 

2196 

2456 

261 

167 

2716 

2976 

3236 

3496 

3755 

4015 

4274 

4533 

4792 

5051 

259 

168 

5309 

5568 

5826 

60S4 

6342 

6600 

6858  • 

7115 

7372 

7630 

258 

169 

7887 

8144 

8400 

8657 

8913 

9170 

9426 

9682 

9938 

*193 

256 

170 

230449 

0704 

0960 

1215 

1470 

1724 

1979 

2234 

2488 

2742 

254 

171 

2996 

3250 

3504 

3757 

4011 

4264 

4517 

4770 

5023 

5276 

253 

172 

5528 

5781 

6033 

6285 

6537 

6789 

7041 

7292 

7544 

7795 

252 

173 

8046 

8297 

8548 

8799 

9049 

9299 

9550 

9800 

**50 

*300 

250 

174 

240549 

0799 

1048 

1297 

1546 

1795 

2044 

2293 

2541 

2790 

249 

175 

3038 

3286 

3534 

3782 

4030 

4277 

4525 

4772 

5019 

5266 

248 

176 

5513 

5759 

6006 

6252 

6499 

6745 

6991 

7237 

7482 

7728 

246 

177 

7973 

8219 

8464 

8709 

8954 

9198 

9443 

9687 

9932 

*176 

245 

178 

250420 

0664 

0908 

1151 

1395 

1638 

1881 

2125 

2368 

2610 

243 

179 

2853 

3096 

3338 

3580 

3822 

4064 

4306 

4548 

4790 

5031 

242 

180 

255273 

5514 

5755 

5996 

6237 

6477 

6718 

6958 

7198 

7439 

241 

181 

7679 

7918 

8158 

8398 

8637 

8877 

9116 

9355 

9594 

9S33 

239 

182 

260071 

0310 

0548 

0787 

1025 

1263 

1501 

1739 

1976 

2214 

238 

183 

2451 

2688 

2925 

3162 

3399 

3636 

3873 

4109 

4346 

4582 

237 

184 

4818 

5054 

5290 

5525 

5761 

5996 

6232 

6467 

6702 

6937 

235 

185 

7172 

7406 

T641 

7875 

8110 

8344 

8578 

8812 

9046 

9279 

234 

186 

9513 

9746 

9980 

*213 

*446 

*679 

*912 

1144 

1377 

1609 

233 

187 

271842 

3074 

2306 

2538 

2770 

3001 

3233 

3464 

3696 

3927 

232 

188 

4158 

4389 

4620 

4850 

5081 

5311 

5542 

5772 

6002 

6232 

230 

189 

6462 

6692 

6921 

7151 

7380 

7609 

7838 

8067 

8296 

8525 

229 

190 

278754 

8982 

9211 

9439 

9667 

9895 

*123 

*351 

*57S 

*S06 

228 

191 

281033 

1261 

1488 

1715 

1942 

2169 

2396 

2622 

2849 

3075 

227 

192 

3301 

3527 

3753 

3979 

4205 

4431 

4656 

4882 

5107 

5332 

226 

193 

5557 

5782 

6007 

6232 

6456 

6681 

6905 

7130' 

7354 

7578 

225 

194 

7802 

8026 

8249 

8473 

8696 

8920 

9143 

9366 

9589 

9812 

223 

195 

290035 

0257 

0480 

0702 

0925 

1147 

1369 

1591 

1813 

2034 

222 

196 

2256 

2478 

2699 

2920 

3141 

3363 

3584 

3S04 

4025 

4246 

221 

197 

4466 

4687 

4907 

5127 

5347 

5567 

5787 

6007 

6226 

6446 

220 

198 

6665 

6884 

7104 

7323 

7542 

7761 

7979 

8198 

8416 

8635 

219 

199 

8853 

9071 

9289 

9507 

9725 

9943 

*161 

*378 

*595 

*S13 

218 

N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

D. 

TABLE   XXIX  (CONTINUED) 


49 


N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

D. 

200 

301030 

1247 

1464 

1681 

1S98 

2114 

2331 

2547 

2764 

2980 

217 

201 

3196 

3412 

3628 

3844 

4059 

4275 

4491 

4706 

4921 

5136 

216 

202 

5351 

5566 

5781 

5996 

6211 

6425 

6639 

6854 

7068 

7282 

215 

203 

7496 

7710 

7924 

8137 

8351 

8564 

8778 

8991 

9204 

9417 

213 

204 

9630 

9843 

**56 

*26S 

*4S1 

*693 

*906 

1118 

1330 

1542 

212 

205 

311754 

1966 

2177 

2389 

2600 

2812 

3023 

3234 

3445 

3656 

211 

206 

3867 

4078 

4289 

4499 

4710 

4920 

5130 

5340 

5551 

5760 

210 

207 

5970 

6180 

6390 

6599 

6809 

7018 

7227 

7436 

7646 

7854 

209 

208 

8063 

8272 

8481 

8689 

8898 

9106 

9314 

9522 

9730 

9938 

208 

209 

320146 

0354 

0562 

0769 

0977 

1184 

1391 

1598 

1805 

2012 

207 

210 

322219 

2426 

2633 

2839 

3046 

3252 

3458 

3665 

3871 

4077 

206 

211 

4282 

4488 

4694 

4899 

5105 

5310 

5516 

5721 

5926 

6131 

205 

212 

6336 

6541 

6745 

6950 

7155 

7359 

7563 

7767 

7972 

8176 

204 

213 

8380 

8583 

8787 

8991 

9194 

9398 

9601 

9805 

***s 

*211 

203 

214 

330414 

0617 

0819 

1022 

1225 

1427 

1630 

1832 

2034 

2236 

202 

215 

2438 

2640 

2842 

3044 

3246 

3447 

3649 

3850 

4051 

4253 

202 

216 

4454 

4655 

4856 

5057 

5257 

5458 

5658 

5859 

6059 

6260 

201 

217 

6460 

6660 

6860 

7060 

7260 

7459 

7659 

7858 

8058 

8257 

200 

218 

8456 

8656 

8855 

9054 

9253 

9451 

9650 

9849 

**47 

*246 

199 

219 

340444 

0642 

0841 

1039 

1237 

1435 

1632 

1830 

2028 

2225 

198 

220 

342423 

2620 

2817" 

3014 

3212 

3409 

3606 

3802 

3999 

4196 

197 

221 

4392 

4589 

4785 

4981 

5178 

5374 

5570 

5766 

5962 

6157 

196 

222 

6353 

6549 

6744 

6939 

7135 

7330 

7525 

7720 

7915 

8110 

195 

223 

8305 

8500 

8694 

8889 

9083 

9278 

9472 

9666 

9860 

**54 

194 

224 

350248 

0442 

0636 

0829 

1023 

1216 

1410 

1603 

1796 

1989 

193 

225 

2183 

2375 

2568 

2761 

2954 

3147 

3339 

3532 

3724 

3916 

193 

226 

4108 

4301 

4493 

4685 

4876 

5068 

5260 

5452 

5643 

5834 

192 

227 

6026 

6217 

6408 

6599 

6790 

6981 

7172 

7363 

75^4 

7744 

191 

228 

7935 

8125 

8316 

8506 

8696 

8886 

9076 

9266 

9456 

9646 

190 

229 

9835 

**25 

*215 

*404 

*593 

*7S3 

*972 

1161 

1350 

1539 

189 

230 

361728 

1917 

2105 

2294 

2482 

2671 

2859 

3048 

3236 

3424 

188 

231 

3612 

3800 

3988 

4176 

4363 

4551 

4739 

4926 

5113 

5301 

188 

232 

5488 

5675 

5862 

6049 

6236 

6423 

6610 

6796 

6983 

7169 

187 

233 

7356 

7542 

7729 

7915 

8101 

8287 

8473 

8659 

8845 

9030 

186 

234 

9216 

9401 

9587 

9772 

9958 

*143 

*328 

*513 

*69S 

*SS3 

185 

235 

371068 

1253 

1437 

1622 

1806 

1991 

2175 

•2360 

2544 

2728 

184 

236 

2912 

3096 

3280 

3464 

3647 

3831 

4015 

4198 

4382 

4565 

184 

237 

4748 

4932 

5115 

5298 

5481 

5664 

5846 

6029 

6212 

6394 

183 

238 

6577 

6759 

6942 

7124 

7306 

7488 

7670 

7852 

8034 

8216 

182 

239 

8398 

8580 

8761 

8943 

9124 

9306 

9487 

9668 

9849 

**30 

181 

240 

380211 

0392 

0573 

0754 

0934 

1115 

1296 

1476 

1656 

1837 

181 

241 

2017 

2197 

2377 

2557 

2737 

2917 

3097 

3277 

3456 

3636 

180 

242 

3815 

3995 

4174 

4353 

4533 

4712 

4891 

5070 

5249 

5428 

179 

243 

5606 

5785 

5964 

6142 

6321 

6499 

6677 

6856 

7034 

7212 

178 

244 

7390 

7568 

7746 

7923 

8101 

8279 

8456 

8634 

8811 

8989 

178 

245 

9166 

9343 

9520 

9698 

9875 

**51 

*228 

*405 

*582 

*759 

177 

246 

390935 

1112 

1288 

1464 

1641 

1817 

1993 

2169 

2345 

2521 

176 

247 

2697 

2873 

3048 

3224 

3400 

3575 

3751 

3926 

4101 

4277 

176 

248 

4452 

4627 

4802 

4977 

5152 

5326 

5501 

5676 

5850 

6025 

175 

249 

6199 

6374 

6548 

6722 

6896 

7071 

7245 

7419 

7592 

7766 

174 

N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

D. 

50 


TABLE  XXIX  (CONTINUED) 


N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

D. 

250 

397940 

8114 

8287 

8461 

8634 

8808 

8981 

9154 

9328 

9501 

173 

251 

9674 

9847 

**20 

*192 

*365 

*538 

*711 

*SS3 

1056 

1228 

173 

252 

401401 

1573 

1745 

1917 

2089 

2261 

2433 

2605 

2777 

2949 

172 

253 

3121 

3292 

3464 

3635 

3807 

3978 

4149 

4320 

4492 

4663 

171 

254 

4834 

5005 

5176 

5346 

5517 

5688 

5858 

6029 

6199 

6370 

171 

255 

6540 

6710 

6881 

7051 

7221 

7391 

7561 

7731 

7901 

8070 

170 

256 

8240 

8410 

8579 

8749 

8918 

9087 

9257 

9426 

9595 

9764 

169 

257 

9933 

*102 

*271 

*440 

*609 

*777 

*946 

1114 

1283 

1451 

169 

258 

411620 

17S8 

1956 

2124 

2293 

2461 

2629 

2796 

2964 

3132 

168 

259 

3300 

3467 

3635 

3803 

3970 

4137 

4305 

4472 

4639 

4806 

167 

260 

414973 

5140 

5307 

5474 

5641 

5808 

5974 

6141 

6308 

6474 

167 

261 

6641 

6807 

6973 

7139 

7306 

7472 

7638 

7804 

7970 

8135 

166 

262 

8301 

8467 

8633 

8798 

8964 

9129 

9295 

9460 

9625 

9791 

165 

263 

9956 

*121 

*286 

*451 

*616 

*781 

*945 

1110 

1275 

1439 

165 

264 

421604 

1788 

1933 

2097 

2261 

2426 

2590 

2754 

2918 

3082 

164 

265 

3246 

3410 

3574 

3737 

-3901 

4065 

4228 

4392 

4555 

4718 

164 

266 

4882 

5045 

5208 

5371 

5534 

5697 

5860 

6023 

61S6 

6349 

163 

267 

6511 

6674 

6836 

6999 

7161 

7324 

7486 

7648 

7811 

7973 

162 

268 

8135 

8297 

8459 

8621 

8783 

8944 

9106 

9268 

9429 

9591 

162 

269 

9752 

9914 

**75 

*236 

*398 

*559 

*720 

*881 

1042 

1203 

161 

270 

431364 

1525 

1685 

1846 

2007 

2167 

2328 

2488 

2649 

2809 

161 

271 

2969 

3130 

3290 

3450 

3610 

3770 

3930 

4090 

4249 

4409 

160 

272 

4569 

4729 

4888 

5048 

5207 

5367 

5526 

5685 

5844 

6004 

159 

273. 

6163 

6322 

6481 

6640 

6798 

6957 

7116 

7275 

7433 

7592 

159 

274 

7751 

7909 

8067 

8226 

8384 

8542 

8701 

8859 

9017 

9175 

158 

275 

9333 

9491 

9648 

9806 

9964 

*122 

*279 

*437 

*594 

*752 

158 

276 

440909 

1066 

1224 

1381 

1538 

1695 

1852 

2009 

2166 

2323 

157 

277 

2480 

.263  7 

2793 

2950 

3106 

3263 

3419 

3576 

3732 

3889 

157 

278 

4045 

4201 

4357 

4513 

4669 

4825 

4981 

5137 

5293 

5449 

156 

279 

5604 

5760 

5915 

6071 

6226 

6382 

6537 

6692 

6848 

7003 

155 

280 

447158 

7313 

7468 

7623 

7778 

7933 

8088 

8242 

8397 

8552 

155 

281 

8706 

8861 

9015 

9170 

9324 

9478 

9633 

9787 

9941 

**95 

154 

282 

450249 

0403 

0557 

0711 

0865 

1018 

1172 

1326 

1479 

1633 

154 

283 

1786 

1940 

2093 

2247 

2400 

2553 

2706 

2859 

3012 

3165 

153 

284 

3318 

3471 

3624 

3777 

3930 

40S2 

4235 

4387 

4540 

4692 

153 

285 

4845 

4997 

5150 

5302 

5454 

5606 

5758 

5910 

6062 

6214 

152 

286 

6366 

6518 

6670 

6821 

6973 

7125 

7276 

7428 

7579 

7731 

152 

287 

7882 

8033 

8184 

8336 

8487 

8638 

8789 

8940 

9091 

9242 

151 

288 

9392 

9543 

9694 

9845 

9995 

*146 

*296 

*447 

*597 

*74S 

151 

289 

460898 

1048 

1198 

1348 

1499 

1649 

1799 

1948 

2098 

2248 

150 

290 

462398 

2548 

2697 

2847 

2997 

3146 

3296 

3445 

3594 

3744 

150 

291 

3893 

4042 

4191 

4340 

4490 

4639 

47S8 

4936 

5085 

5234 

149 

292 

5383 

5532 

5680 

5829 

5977 

6126 

6274 

6423 

6571 

6719 

149 

293 

6868 

7016 

7164 

7312 

7460 

7608 

7756 

7904 

8052 

8200 

148 

294 

8347 

8495 

8643 

8790 

8938 

9085 

9233 

9380 

9527 

9675 

148 

295 

9822 

9969 

*116 

*263 

*410 

*557 

*704 

*851 

*99S 

1145 

147 

296 

471292 

1438 

1585 

1732 

1878 

2025 

2171 

2318 

2464 

2610 

146 

297 

2756 

2903 

3049 

3195 

3341 

3487 

3633 

3779 

3925 

4071 

146 

298 

4216 

4362 

4508 

4653 

4799 

4944 

5090 

5235 

5381 

5526 

146 

299 

5671 

5816 

5962 

6107 

6252 

6397 

6542 

6687 

6832 

6976 

145 

N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

D. 

TABLE  XXIX  (CONTINUED) 


51 


N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

D. 

300 

477121 

7266 

7411 

7555 

7700 

7844 

7989 

8133 

8278 

8422 

145 

301 

8566 

8711 

8855 

8999 

9143 

9287 

9431 

9575 

9719 

9863 

144 

302 

480007 

0151 

0294 

0438 

0582 

0725 

0869 

1012 

1156 

1299 

144 

303 

1443 

1586 

1729 

1872 

2016 

2159 

2302 

2445 

2588 

2731 

143 

304 

2874 

3016 

3159 

3302 

3445 

3587 

3730 

3872 

4015 

4157 

143 

305 

4300 

4442 

4585 

4727 

4869 

5011 

5153 

5295 

5437 

5579 

142 

306 

5721 

5863 

6005 

6147 

6289 

6430 

6572 

6714 

6855 

6997 

142 

307 

7138 

7280 

7421 

7563 

7704 

7845 

7986 

8127 

8269 

8410 

141 

308 

8551 

8692 

8833 

8974 

9114 

9255 

9396 

9537 

9677 

9818 

141 

309 

9958 

**99 

*239 

*380 

*520 

*661 

*801 

#941 

1081 

1222 

140 

310 

491362 

1502 

1642 

1782 

1922 

2062 

2201 

2341 

2481 

2621 

140 

311 

2760 

2900 

3040 

3179 

3319 

3458 

3597 

3737 

3876 

4015 

139 

312 

4155 

4294 

4433 

4572 

4711 

4850 

4989 

5128 

5267 

5406 

139 

313 

5544 

5683 

5822 

5960 

6099 

6238 

6376 

6515 

6653 

6791 

139 

314 

6930 

7068 

7206 

7344 

7483 

7621 

7759 

7897 

8035 

8173 

138 

315 

8311 

8448 

8586 

8724 

8862 

8999 

9137 

9275 

9412 

9550 

138 

316 

9687 

9824 

9962 

**99 

*236 

*374 

*511 

*64S 

*785 

*922 

137 

317 

501059 

1196 

1333 

1470 

1607 

1744 

1880 

2017 

2154 

2291 

137 

318 

2427 

2564 

2700 

2837 

2973 

3109 

3246 

3382 

3518 

3655 

136 

319 

3791 

3927 

4063 

4199 

4335 

4471 

4607 

4743 

4878 

5014 

136 

320 

505150 

5286 

5421 

5557 

5693 

5828 

5964 

6099 

6234 

6370 

136 

321 

6505 

6640 

6776 

6911 

7046 

7181 

7316 

7451 

7586 

7721 

135 

322 

7856 

7991 

8126 

8260 

8395 

8530 

8664 

8799 

8934 

9068 

135 

323 

9203 

9337 

9471 

9606 

9740 

9874 

*#*9 

*143 

*277 

*411 

134 

324 

510545 

0679 

0813 

0947 

1081 

1215 

1349 

1482 

1616 

1750 

134 

325 

1883 

2017 

2151 

2284 

2418 

2551 

2684 

2818 

2951 

3084 

133 

326 

3218 

3351 

3484 

3617 

3750 

3883 

4016 

4149 

4282 

4414 

133 

327 

4548 

4681 

4813 

4946 

5079 

5211 

5344 

5476 

5609 

5741 

133 

328 

5874 

6006 

6139 

6271 

6403 

6535 

6668 

6800 

6932 

7064 

132 

329 

7196 

7328 

7460 

7592 

7724 

7855 

7987 

8119 

8251 

8382 

132 

330 

518514 

8646 

8777 

8909 

9040 

9171 

9303 

9434 

9566 

9697 

131 

331 

9828 

9959 

**90 

*221 

*353 

*4S4 

*615 

*745 

*876 

1007 

131 

332 

521138 

1269 

1400 

1530 

1661 

1792 

1922 

2053 

2183 

2314 

131 

333 

2444 

2575 

2705 

2835 

2966 

3096 

3226 

3356 

3486 

3616 

130 

334 

3746 

3876 

4006 

4136 

4266 

4396 

4526 

4656 

4785 

4915 

130 

335 

5045 

5174 

5304 

5434 

5563 

5693 

5822 

5951 

6081 

6210 

129 

336 

6339 

6469 

6598 

6727 

6856 

6985 

7114 

7243 

7372 

7501 

129 

337 

7630 

7759 

7888 

8016 

8145 

8274 

8402 

8531 

8660 

8788 

129 

338 

8917 

9045 

9174 

9302 

9430 

9559 

9687 

9815 

9943 

**72 

128 

339 

530200 

0328 

0456 

0584 

0712 

0840 

0968 

1096 

1223 

1351 

128 

340 

531479 

1607 

1734 

1862 

1990 

2117 

2245 

2372 

2500 

2627 

128 

341 

2754 

2882 

3009 

3136 

3264 

3391 

3518 

3645 

3772 

3899 

127 

342 

4026 

4153 

4280 

4407 

4534 

4661 

4787 

4914 

5041 

5167 

127 

343 

5294 

5421 

5547 

5674 

5800 

5927 

6053 

6180 

6306 

6432 

126 

344 

6558 

6685 

6811 

6937 

7063 

7189 

7315 

7441 

7567 

7693 

126 

345 

7819 

7945 

8071 

8197 

8322 

8448 

8574 

8699 

8825 

8951 

126 

346 

9076 

9202 

9327 

9452 

9578 

9703 

9829 

9954 

**79 

*204 

125 

347 

540329 

0455 

0580 

0705 

0830 

0955 

1080 

1205 

1330 

1454 

125 

348 

1579 

1704 

1829 

1953 

2078 

2203 

2327 

2452 

2576 

2701 

125 

349 

2825 

2950 

3074 

3199 

3323 

3447 

3571 

3696 

3820 

3944 

124 

N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

D. 

52 


TABLE  XXIX  (CONTINUED) 


N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

D. 

350 

544068 

4192 

4316 

4440 

4564 

4688 

4812 

4936 

5060 

5183 

124 

351 

5307 

5431 

5555 

5678 

5802 

5925 

6049 

6172 

6296 

6419 

124 

352 

6543 

6666 

6789 

6913 

7036 

7159 

7282 

7405 

7529 

7652 

123 

353 

7775 

7898 

8021 

8144 

8267 

83S9 

8512 

8635 

8758 

8881 

123 

354 

9003 

9126 

9249 

9371 

9494 

9616 

9739 

9861 

9984 

*106 

123 

355 

550228 

0351 

0473 

0595 

0717 

0840 

0962 

1084 

1206 

1328 

122 

356 

1450 

1572 

1694 

1816 

1938 

2060 

2181 

2303 

2425 

2547 

122 

357 

2668 

2790 

2911 

3033 

3155 

3276 

3398 

3519 

3640 

3762 

121 

358 

3883 

4004 

4126 

4247 

4368 

4489 

4610 

4731 

4852 

4973 

121 

359 

5094 

5215 

5336 

5457 

5578 

5699 

5820 

5940 

6061 

6182 

121 

360 

556303 

6423 

6544 

6664 

6785 

6905 

7026 

7146 

7267 

7387 

120 

361 

7507 

7627 

7748 

7868 

7988 

8108 

8228 

8349 

8469 

8589 

120 

362 

8709 

8829 

8948 

9068 

9188 

9308 

9428 

9548 

9667 

9787 

120 

363 

9907 

**26 

*146 

*265 

*385 

*504 

*624 

*743 

*863 

*982 

119 

364 

561101 

1221 

1340 

1459 

1578 

1698 

1817 

1936 

2055 

2174 

119 

365 

2293 

2412 

2531 

2650 

2769 

2887 

3006 

3125 

3244 

3362 

119 

366 

3481 

3600 

3718 

3837 

3955 

4074 

4192 

4311 

4429 

4548 

119 

367 

4666 

4784 

4903 

5021 

5139 

5257 

5376 

5494 

5612 

5730 

118 

368 

5848 

5966 

6084 

6202 

6320 

6437 

6555 

6673 

6791 

6909 

118 

369 

7026 

7144 

7262 

7379 

7497 

7614 

7732 

7849 

7967 

8084 

118 

370 

568202 

8319 

8436 

8554 

8671 

8788 

8905 

9023 

9140 

9257 

117 

371 

9374 

9491 

9608 

9725 

9842 

9959 

**76 

*193 

*309 

*426 

117 

372 

570543 

0660 

0776 

0893 

1010 

1126 

1243 

1359 

1476 

1592 

117 

373 

1709 

1825 

1942 

2058 

2174 

2291 

2407 

2523 

2639 

2755 

116 

574 

2872 

2988 

3104 

3220 

3336 

3452 

3568 

3684 

3800 

3915 

116 

375 

4031 

4147 

4263 

4379 

4494 

4610 

4726 

4841 

4957 

5072 

116 

376 

5188 

5303 

5419 

5534 

5650 

5765 

5880 

5996 

6111 

6226 

115 

377 

6341 

6457 

6572 

6687 

6802 

6917 

7032 

7147 

7262 

7377 

115 

378 

7492 

7607 

7722 

7836 

7951 

8066 

8181 

8295 

8410 

8525 

115 

379 

8639 

8754 

8868 

8983 

9097 

9212 

9326 

9441 

9555 

9669 

114 

>  380 

579784 

9898 

**12 

*126 

*241 

*355 

*469 

*5S3 

*697 

*811 

114 

381 

580925 

1039 

1153 

1267 

1381 

1495 

1608 

1722 

1836 

1950 

114 

382 

2063 

2177 

2291 

2404 

2518 

2631 

2745 

2858 

2972 

3085 

114 

383 

3199 

3312 

3426 

3539 

3652 

3765 

3879 

3992 

4105 

4218 

113 

384 

4331 

4444 

4557 

4670 

4783 

4896 

5009 

5122 

5235 

5348 

113 

385 

5461 

5574 

5686 

5799 

5912 

6024 

6137 

6250 

6362 

6475 

113 

386 

6587 

6700 

6812 

6925 

7037 

7149 

7262 

7374 

7486 

7599 

112 

387 

7711 

7823 

7935 

8047 

8160 

8272 

8384 

8496 

8608 

8720 

112 

388 

8832 

8944 

9056 

9167 

9279 

9391 

9503 

9615 

9726 

9838 

112 

389 

9950 

**61 

*173 

*2S4 

*396 

*507 

*619 

*730 

*842 

*953 

112 

390 

591065 

1176 

1287 

1399 

1510 

1621 

1732 

1843 

1955 

2066 

111 

391 

2177 

2288 

2399 

2510 

2621 

2732 

2843 

2954 

3064 

3175 

111 

392 

3286 

3397 

3508 

3618 

3729 

3840 

3950 

4061 

4171 

4282 

111 

393 

4393 

4503 

4614 

4724 

4834 

4945 

5055 

5165 

5276 

5386 

110 

394 

5496 

5606 

5717 

5827 

5937 

6047 

61-57 

6267 

6377 

6487 

110 

395 

6597 

6707 

6817 

6927 

7037 

7146 

7256 

7366 

7476 

7586 

110 

396 

7695 

7805 

7914 

8024 

8134 

8243 

8353 

8462 

8572 

8681 

110 

397 

8791 

8900 

9009 

9119 

9228 

9337 

9446 

9556 

9665 

9774 

109 

398 

9883 

9992 

*101 

*210 

*319 

*428 

*537 

*646 

*755 

*S64 

109 

399 

600973 

1082 

1191 

1299 

1408 

1517 

1625 

1734 

1843 

1951 

109 

N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

D. 

TABLE  XXIX  (CONTINUED) 


53 


N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

D.. 

400 

602060 

2169 

2277 

2386 

2494 

2603 

2711 

2819 

2928 

3036 

108 

401 

3144 

3253 

3361 

3469 

3577 

3$S6 

3794 

3902 

4010 

4118 

108 

402 

4226 

4334 

4442 

4550 

4658 

4766 

4874 

4982 

5089 

5197 

108 

403 

5305 

5413 

5521 

5628 

5736 

5844 

5951 

6059 

6166 

6274 

108 

404 

6381 

6489 

6596 

6704 

6811 

6919 

7026 

7133 

7241 

7348 

107 

405 

7455 

7562 

7669 

7777 

7884 

7991 

8098 

8205 

8312 

8419 

107 

406 

8526 

8633 

8740 

8847 

8954 

9061 

9167 

9274 

9381 

9488 

107 

407 

9594 

9701 

9808 

9914 

**21 

*128 

*234 

*341 

*447 

*554 

107 

408 

610660 

0767 

0873 

0979 

1086 

1192 

1298 

1405 

1511 

1617 

106 

409 

1723 

1829 

1936 

2042 

2148 

2254 

2360 

2466 

2572 

2678 

106 

410 

612784 

2890 

2996 

3102 

3207 

3313 

3419 

3525 

3630 

3736 

106 

411 

3842 

3947 

4053 

4159 

4264 

4370 

4475 

4581 

4686 

4792 

106 

412 

4897 

5003 

5108 

5213 

5319 

5424 

5529 

5634 

5740 

5845 

105 

413 

5950 

6055 

6160 

6265 

6370 

6476 

6581 

6686 

6790 

6895 

105 

414 

7000 

7105 

7210 

7315 

7420. 

7525 

7629 

7734 

7839 

7943 

105 

415 

8048 

8153 

8257 

8362 

8466 

8571 

8676 

8780 

8884 

8989 

105 

416 

9093 

9198 

9302 

9406 

9511 

9615 

9719 

9824 

9928 

**32 

104 

417 

620136 

0240 

0344 

0448 

0552 

0656 

0760 

0864 

0968 

1072 

104 

418 

1176 

1280 

1384 

1488 

1592 

1695 

1799 

1903 

2007 

2110 

104 

419 

2214 

2318 

2421 

2525 

2628 

2732 

2835 

2939 

3042 

3146 

104 

420 

623249 

3353 

3456 

3559 

3663 

3766 

3869 

3973 

4076 

4179 

103 

421 

4282 

4385 

4488 

4591 

4695 

4798 

4901 

5004 

5107 

5210 

103 

422 

5312 

5415 

5518 

5621 

5724 

5827 

5929 

6032 

6135 

6238 

103 

423 

6340 

6443 

6546 

6648 

6751 

6853 

6956 

7058 

7161 

7263 

103 

424 

7366 

7468 

7571 

7673 

7775 

7878 

7980 

8082 

8185 

8287 

102 

425 

8389 

8491 

8593 

8695 

8797 

8900 

9002 

9104 

9206 

9308 

102 

426 

9410 

9512 

9613 

9715 

9817 

9919 

**21 

*123 

*224 

*326 

102 

427 

630428 

0530 

0631 

0733 

0835 

0936 

1038 

1139 

1241 

1342 

102 

428 

1444 

1545 

1647 

1748 

1849 

1951 

2052 

2153 

2255 

2356 

101 

429 

2457 

2559 

2660 

2761 

2862 

2963 

3064 

3165 

3266 

3367 

101 

430 

633468 

3569 

3670 

3771 

3872 

3973 

4074 

4175 

4276 

4376 

100 

431 

4477 

4578 

4679 

4779 

4880 

4981 

5081 

5182 

5283 

5383 

100 

432 

5484 

5584 

5685 

5785 

5886 

5986 

6087 

6187 

6287 

6388 

100 

433 

6488 

6588 

6688 

6789 

6889 

6989 

7089 

7189 

7290 

7390 

100 

434 

7490 

7590 

7690 

7790 

7890 

7990 

8090 

8190 

8290 

8389 

99 

435 

8489 

8589 

8689 

8789 

8888 

8988 

9088 

9188 

9287 

9387 

99 

436 

9486 

9586 

9686 

9785 

9885 

9984 

**S4 

*183 

*283 

*3S2 

99 

437 

640481 

0581 

0680 

0779 

0879 

0978 

1077 

1177 

1276 

1375 

99 

438 

1474 

1573 

1672 

1771 

1871 

1970 

2069 

2168 

2267 

2366 

99 

439 

2465 

2563 

2662 

2761 

2860 

2959 

3058 

3156 

3255 

3354 

99 

440 

643453 

3551 

3650 

3749 

3847 

3946 

4044 

4143 

4242 

4340 

98 

441 

4439 

4537 

4636 

4734 

4832 

4931 

5029 

5127 

5226 

5324 

98 

442 

5422 

5521 

5619 

5717 

5815 

5913 

6011 

6110 

6208 

6306 

98 

443 

6404 

6502 

6600 

6698 

6796 

6894 

6992 

7089 

7187 

7285 

98 

444 

7383 

7481 

7579 

7676 

7774 

7872 

7969 

8067 

8165 

8262 

98 

445 

8360 

8458 

8555 

8653 

8750 

8848 

8945 

9043 

9140 

9237 

97 

446 

9335 

9432 

9530 

9627 

9724 

9821 

9919 

**16 

*113 

*210 

97 

447 

650308 

0405 

0502 

0599 

0696 

0793 

0890 

0987 

1084 

1181 

97 

448 

1278 

1375 

1472 

1569 

1666 

1762 

1859 

1956 

2053 

2150 

97 

449 

2246 

2343 

2440 

2536 

2633 

2730 

2826 

2923 

3019 

3116 

97 

N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

D. 

54 


TABLE  XXIX  (CONTINUED) 


N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

D. 

450 

653213 

3309 

3405 

3502 

3598 

3695 

3791 

3888 

3984 

4080 

96 

451 

4177 

4273 

4369 

4465 

4562 

4658 

4754 

4850 

4946 

5042 

96 

452 

5138 

5235 

5331 

5427 

5523 

5619 

5715 

5810 

5906 

6002 

96 

453 

6098 

6194 

6290 

6386 

6482 

6577 

6673 

6769 

6864 

6960 

96 

454 

7056 

7152 

7247 

7343 

7438 

7534 

7629 

7725 

7820 

7916 

96 

455 

8011 

8107 

8202 

8298 

8393 

8488 

8584 

8679 

8774 

8870 

95 

456 

8965 

9060 

9155 

9250 

9346 

9441 

9536 

9631 

9726 

9821 

95 

457 

9916 

**11 

*106 

*201 

*296 

*391 

*4S6 

*5S1 

*676 

*771 

95 

458 

660865 

0960 

1055 

1150 

1245 

1339 

1434 

1529 

1623 

1718 

95 

459 

1813 

1907 

2002 

2096 

2191 

22S6 

2380 

2475 

2569 

2663 

95 

460 

662758 

2852 

2947 

3041 

3135 

3230 

3324 

3418 

3512 

3607 

94 

461 

3701 

3795 

3889 

3983 

4078 

4172 

4266 

4360 

4454 

4548 

94 

462 

4642 

4736 

4830 

4924 

5018 

5112 

5206 

5299 

5393 

5487 

94 

463 

5581 

5675 

5769 

5862 

5956 

6050 

6143 

6237 

6331 

6424 

94 

464 

6518 

6612 

6705 

6799 

6892 

6986 

7079 

7173 

7266 

7360 

94 

465 

7453 

7546 

7640 

7733 

7826 

7920 

8013 

8106 

8199 

8293 

93 

466 

8386 

8479 

8572 

8665 

8759 

8852 

8945 

9038 

9131 

9224 

93 

467 

9317 

9410 

9503 

9596 

9689 

9782 

9875 

9967 

**60 

*153 

93 

468 

670246 

0339 

0431 

0524 

0617 

0710 

0802 

0895 

0988 

1080 

93 

469 

1173 

1265 

1358 

1451 

1543 

1636 

1728 

1821 

1913 

2005 

93 

470 

672098 

2190 

2283 

2375 

2467 

2560 

2652 

2744 

2836 

2929 

92 

471 

3021 

3113 

3205 

3297 

3390 

3482 

3574 

3666 

3758 

3850 

92 

472 

3942 

4034 

4126 

4218 

4310 

4402 

4494 

4586 

4677 

4769 

92 

473 

4861 

4953 

5045 

5137 

5228 

5320 

5412 

5503 

5595 

5687 

92 

474 

5778 

5870 

5962 

6053 

6145 

6236 

6328 

6419 

6511 

6602 

92 

475 

6694 

6785 

6876 

6068 

7059 

7151 

7242 

7333 

7424 

7516 

91 

476 

7607 

7698 

7789 

7881 

7972 

8063 

8154 

8245 

8336 

8427 

91 

477 

8518 

8609 

8700 

8791 

8882 

8973 

9064 

9155 

9246 

9337 

91 

478 

9428 

9519 

9610 

9700 

9791 

9882 

9973 

**63 

*154 

*245 

91 

479 

680336 

0426 

0517 

0607 

0698 

0789 

0879 

0970 

1060 

1151 

91 

480 

681241 

1332 

1422 

1513 

1603 

1693 

1784 

1874 

1964 

2055 

90 

481 

2145 

2235 

2326 

2416 

2506 

2596 

2686 

2777 

2867 

2957 

90 

482 

3047 

3137 

3227 

3317 

3407 

3497 

3587 

3677 

3767 

3857 

90 

483 

3947 

4037 

4127 

4217 

4307 

4396 

4486 

4576 

4666 

4756 

90 

484 

4845 

4935 

5025 

5114 

5204 

5294 

5383 

5473 

5563 

5652 

90 

485 

5742 

5831 

5921 

6010 

6100 

6189 

6279 

6368 

6458 

6547 

89 

486 

6636 

6726 

6815 

6904 

6994 

7083 

7172 

7261 

7351 

7440 

89 

487 

7529 

7618 

7707 

7796 

7886 

7975 

8064 

8153 

8242 

8331 

89 

488 

8420 

8509 

8598 

8687 

8776 

8865 

8953 

9042 

9131 

9220 

89 

489 

9309 

9398 

9486 

9575 

9664 

9753 

9841 

9930 

**19 

*107 

89 

490 

690196 

0285 

0373 

0462 

0550 

0639 

0728 

0816 

0905 

0993 

89 

491 

1081 

1170 

1258 

1347 

1435 

1524 

1612 

1700 

1789 

1877 

88 

492 

1965 

2053 

2142 

2230 

2318 

2406 

2494 

2583 

2671 

2759 

88 

493 

2847 

2935 

3023 

3111 

3199 

3287 

3375 

3463 

3551 

3639 

88 

494 

3727 

3815 

3903 

3991 

4078 

4166 

4254 

4342 

4430 

4517 

88 

495 

4605 

4693 

4781 

4868 

4956 

5044 

5131 

5219 

5307 

5394 

88 

496 

5482 

5569 

5657 

5744 

5832 

5919 

6007 

6094 

6182 

6269 

87 

497 

6356 

6444 

6531 

6618 

6706 

6793 

6880 

6968 

7055 

7142 

87 

498 

7229 

7317 

7404 

7491 

7578 

7665 

7752 

7839 

7926 

8014 

87 

499 

8101 

8188 

8275 

8362 

8449 

8535 

8622 

8709 

8796 

8883 

87 

N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

D. 

TABLE  XXIX  (CONTINUED) 


55 


N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

D. 

500 

698970 

9057 

9144 

9231 

9317 

9404 

9491 

9578 

9664 

9751 

87 

501 

9838 

9924 

**11 

**9S 

*184 

*271 

*35S 

*444 

*531 

*617 

87 

502 

700704 

0790 

0877 

0963 

1050 

1136 

1222 

1309 

1395 

1482 

86 

503 

1568 

1654 

1741 

1827 

1913 

1999 

2086 

2172 

2258 

2344 

86 

504 

2431 

2517 

2603 

2689 

2775 

2861 

2947 

3033 

3119 

3205 

86 

505 

3291 

3377 

3463 

3549 

3635 

3721 

3807 

3893 

3979 

4065 

86 

506 

4151 

4236 

4322 

4408 

4494 

4579 

4665 

4751 

4837 

4922 

86 

507 

5008 

5094 

5179 

5265 

5350 

5436 

5522 

5607 

5693 

5778 

86 

508 

5864 

5949 

6035 

6120 

6206 

6291 

6376 

6462 

6547 

6632 

85 

509 

6718 

6803 

6888 

6974 

7059 

7144 

7229 

7315 

7400 

7485 

85 

510 

707570 

7655 

7740 

7826 

7911 

7996 

8081 

8166 

8251 

8336 

85 

511 

8421 

8506 

8591 

8676 

8761 

8846 

8931 

9015 

9100 

9185 

85 

512 

9270 

9355 

9440 

9524 

9609 

9694 

9779 

9863 

9948 

**33 

85 

513 

710117 

0202 

0287 

0371 

0456 

0540 

0625 

0710 

0794 

0879 

85 

514 

0963 

1048 

1132 

1217 

1301 

1385 

1470 

1554 

1639 

1723 

84 

515 

1807 

1892 

1976 

2060 

2144 

2229 

2313 

2397 

2481 

2566 

84 

516 

2650 

2734 

2818 

2902 

2986 

3070 

3154 

3238 

3323 

3407 

84 

517 

3491 

3575 

3659 

3742 

3826 

3910 

3994 

4078 

4162 

4246 

84 

518 

4330 

4414 

4497 

4581 

4665 

4749 

4833 

4916 

5000 

5084 

84 

519 

5167 

5251 

5335 

5418 

5502 

5586 

5669 

5753 

5836 

5920 

84 

520 

716003 

6087 

6170 

6254 

6337 

6421 

6504 

6588 

6671 

6754 

83 

521 

6838 

6921 

7004 

7088 

7171 

7254 

7338 

7421 

7504 

7587 

83 

522 

7671 

7754 

7837 

7920 

8003 

8086 

8169 

8253 

8336 

8419 

83 

523 

8502 

8585 

8668 

8751 

8834 

8917 

9000 

9083 

9165 

9248 

83 

524 

9331 

9414 

9497 

9580 

9663 

9745 

9828 

9911 

9994 

**77 

83 

525 

720159 

0242 

0325 

0407 

0490 

0573 

0655 

0738 

0821 

0903 

83 

526 

0986 

1068 

1151 

1233 

1316 

1398 

1481 

1563 

1646 

1728 

82 

527 

1811 

1893 

1975 

2058 

2140 

2222 

2305 

2387 

2469 

2552 

82 

528 

2634 

2716 

2798 

2881 

2963 

3045 

3127 

3209 

3291 

3374 

82 

529 

3456 

3538 

3620 

3702 

3784 

3866 

3948 

4030 

4112 

4194 

82 

530 

724276 

4358 

4440 

4522 

4604 

4685 

4767 

4849 

4931 

5013 

82 

531 

5095 

5176 

5258 

5340 

5422 

5503 

5585 

5667 

5748 

5830 

82 

532 

5912 

5993 

6075 

6156 

6238 

6320 

6401 

6483 

6564 

6646 

82 

533 

6727 

6809 

6890 

6972 

7053 

7134 

7216 

7297 

7379 

7460 

81 

534 

7541 

7623 

7704 

7785 

7866 

7948 

8029 

8110 

8191 

8273 

81 

535 

8354 

8435 

8516 

8597 

8678 

8759 

8841 

8922 

9003 

9084 

81 

536 

9165 

9246 

9327 

9408 

9489 

9570 

9651 

9732 

9813 

9893 

81 

537 

9974 

**55 

*136 

*217 

*298 

*378 

*459 

*540 

*621 

*702 

81 

538 

730782 

0863 

0944 

1024 

1105 

1186 

1266 

1347 

1428 

1508 

81 

539 

1589 

1669 

1750 

1830 

1911 

1991 

2072 

2152 

2233 

2313 

81 

540 

732394 

2474 

2555 

2635 

2715 

2796 

2876 

2956 

3037 

3117 

80 

541 

3197 

3278 

3358 

3438 

3518 

3598 

3679 

3759 

3839 

3919 

80 

542 

3999 

4079 

4160 

4240 

4320 

4400 

4480 

4560 

4640 

4720 

80 

543 

4800 

4880 

4960 

5040 

5120 

5200 

5279 

5359 

5439 

5519 

80 

544 

5599 

5679 

5759 

5838 

5918 

5998 

6078 

6157 

6237 

6317 

80 

545 

6397 

6476 

6556 

6635 

6715 

6795 

6874 

6954 

7034 

7113 

80 

546 

7193 

7272 

7352 

7431 

7511 

7590 

7670 

7749 

7829 

7908 

79 

547 

7987 

8067 

8146 

8225 

8305 

8384 

8463 

8543 

8622 

8701 

79 

548 

8781 

8860 

8939 

9018 

9097 

9177 

.9256 

9335 

9414 

9493 

79 

549 

9572 

9651 

9731 

9810 

9889 

9968 

**47 

*126 

*205 

*284 

79 

N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

D. 

56 


TABLE  XXIX  (CONTINUED) 


N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

D. 

550 

740363 

0442 

0521 

0600 

0678 

0757 

0836 

0915 

0994 

1073 

79 

551 

1152 

1230 

1309 

1388 

1467 

1546 

1624 

1703 

17S2 

I860 

79 

552 

1939 

2018 

2096 

2175 

2254 

2332 

2411 

2489 

25  68 

2647 

79 

553 

2725 

2804 

2882 

2961 

3039 

3118 

3196 

3275 

3353 

3431 

78 

554 

3510 

3588 

3667 

3745 

3823 

3902 

39SO 

4058 

4136 

4215 

78 

555 

4293 

4371 

4449 

4528 

4606 

4684 

4762 

4840 

4919 

4997 

78 

556 

5075 

5153 

5231 

5309 

5387 

5465 

5543 

5621 

5699 

5777 

78 

557 

5855 

5933 

6011 

6089 

6167 

6245 

6323 

6401 

6479 

6556 

78 

558 

6634 

6712 

6790 

6868 

6945 

7023 

7101 

7179 

7256 

7334 

78 

559 

7412 

7489 

7567 

7645 

7722 

7800 

7878 

7955 

8033 

8110 

78 

560 

748188 

8266 

8343 

8421 

8498 

8576 

8653 

8731 

8808 

8885 

77 

561 

8963 

9040 

9118 

9195 

9272 

9350 

9427 

9504 

9582 

9659 

77 

562 

9736 

9814 

9891 

9968 

**45 

*123 

*200 

*277 

*354 

*431 

77 

563 

750508 

0586 

0663 

0740 

0817 

0894 

0971 

1048 

1125 

1202 

77 

564 

1279 

1356 

1433 

1510 

1587 

1664 

1741 

1818 

1895 

1972 

77 

565 

2048 

2125 

2202 

2279 

2356 

2433 

2509 

2586 

2663 

2740 

77 

566 

2816 

2893 

2970 

3047 

3123 

3200 

3277 

3353 

3430 

3506 

77 

567 

3583 

3660 

3736 

3813 

3889 

3966 

4042 

4119 

4195 

4272 

77 

568 

4348 

4425 

4501 

4578 

4654 

4730 

4807 

4883 

4960 

5036 

76 

569 

5112 

5189 

5265 

5341 

5417 

5494 

5570 

5646 

5722 

5799 

76 

570 

755875 

5951 

6027 

6103 

6180 

6256 

6332 

6408 

6484 

6560 

76 

571 

6636 

6712 

6788 

6864 

6940 

7016 

7092 

7168 

7244 

7320 

76 

572 

7396 

7472 

7548 

7624 

7700 

7775 

7851 

7927 

8003 

8079 

76 

573 

8155 

8230 

8306 

8382 

8458 

8533 

8609 

8685 

8761 

8836 

76 

574 

8912 

8988 

9063 

9139 

9214 

9290 

9366 

9441 

9517 

9592 

76 

'  575 

9668 

9743 

9819 

9894 

9970 

**45 

*121 

*196 

•*272 

*347 

75 

576 

760422 

0498 

0573 

0649 

0724 

0799 

0875 

0950 

1025 

1101 

75 

577 

1176 

1251 

1326 

1402 

1477 

1552 

1627 

1702 

1778 

1853 

75 

578 

1928 

2003 

2078 

2153 

2228 

2303 

2378 

2453 

2529 

2604 

75 

579 

2679 

2754 

2829 

2904 

2978 

3053 

3128 

3203 

3278 

3353 

75 

580 

763428 

3503 

3578 

3653 

3727 

3802 

3877 

3952 

4027 

4101 

75 

581 

4176 

4251 

4326 

4400 

4475 

4550 

4624 

4699 

4774 

4848 

75 

582 

4923 

4998 

5072 

5147 

5221 

5296 

5370 

5445 

5520 

5594 

75 

583 

5669 

5743 

5818 

5892 

5966 

6041 

6115 

6190 

6264 

6338 

74 

584 

6413 

6487 

6562 

6636 

6710 

6785 

6859 

6933 

7007 

7082 

74 

585 

7156 

7230 

7304 

7379 

7453 

7527 

7601 

7675 

7749 

7823 

74 

586 

7898 

7972 

8046 

8120 

8194 

8268 

8342 

8416 

8490 

8564 

74 

587 

8638 

8712 

8786 

8860 

8934 

9008 

9082 

9156 

9230 

9303 

74 

588 

9377 

9451 

9525 

9599 

9673 

9746 

9820 

9894 

9968 

**42 

74 

589 

770115 

0189 

0263 

0336 

0410 

0484 

0557 

0631 

0705 

0778 

74 

590 

770852 

0926 

0999 

1073 

1146 

1220 

1293 

1367 

1440 

1514 

74 

591 

1587 

1661 

1734 

1808 

1881 

1955 

2028 

2102 

2175 

2248 

73 

592 

2322 

2395 

2468 

2542 

2615 

2688 

2762 

2835 

2908 

2981 

73 

593 

3055 

3128 

3201 

3274 

3348 

3421 

3494 

3567 

36iO 

3713 

73 

594 

3786 

3860 

3933 

4006 

4079 

4152 

4225 

4298 

'4371 

4444 

73 

595 

4517 

4590 

4663 

4736 

4809 

4882 

4955 

5028 

5100 

5173 

73 

596 

5246 

5319 

5392 

5465 

5538 

5610 

5683 

5756 

5829 

5902 

73 

597 

5974 

6047 

6120 

6193 

6265 

6338 

6411 

6483 

6556 

6629 

73 

598 

6701 

6774 

6846 

6919 

6992 

7064 

7137 

7209 

7282 

7354 

73 

599 

7427 

7499 

7572 

7644 

7717 

7789 

7862 

7934 

8006 

8079 

72 

N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

D. 

TABLE  XXIX  (CONTINUED) 


57 


N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

D. 

600 

778151 

8224 

8296 

8368 

8441 

8513 

8585 

8658 

8730 

8802 

72 

601 

8874 

8947 

9019 

9091 

9163 

9236 

9308 

9380 

9452 

9524 

72 

602 

9596 

9669 

9741 

9813 

9885 

9957 

**29 

*101 

*173 

*245 

72 

603 

780317 

0389 

0461 

0533 

0605 

0677 

0749 

0821 

0893 

0965 

72 

604 

14)37 

1109 

1181 

1253 

1324 

1396 

1468 

1540 

1612 

1684 

72 

605 

1755 

1827 

1899 

1971 

2042 

2114 

2186 

2258 

2329 

2401 

72 

606 

2473 

2544 

2616 

2688 

2759 

2831 

2902 

2974 

3046 

3117 

72 

607 

3189 

3260 

3332 

3403 

3475 

3546 

3618 

3689 

3761 

3832 

71 

608 

3904 

3975 

4046 

4118 

4189 

4261 

4332 

4403 

4475 

4546 

71 

609 

4617 

4689 

4760 

4831 

4902 

4974 

5045 

5116 

5187 

5259 

71 

610 

785330 

5401 

5472 

5543 

5615 

5686 

5757 

5828 

5899 

5970 

71 

611 

6041 

6112 

6183 

6254 

6325 

6396 

6467 

6538 

6609 

6680 

71 

612 

6751 

6822 

6893 

6964 

7035 

7106 

7177 

7248 

7319 

7390 

71 

613 

7460 

7531 

7602 

7673 

7744 

7815 

7885 

7956 

8027 

8098 

71 

614 

8168 

8239 

8310 

8381 

8451 

8522 

8593 

8663 

8734 

8804 

71 

615 

8875 

8946 

9016 

9087 

9157 

9228 

9299 

9369 

9440 

9510 

71 

616 

9581 

9651 

9722 

9792 

9863 

9933 

***4 

**74 

*144 

*215 

70 

617 

790285 

0356 

0426 

0496 

0567 

0637 

0707 

0778 

0848 

0918 

70 

618 

0988 

1059 

1129 

1199 

1269 

1340 

1410 

1480 

1550 

1620 

70 

619 

1691 

1761 

1831 

1901 

1971 

2041 

2111 

2181 

2252 

2322 

70 

620 

792392 

2462 

2532 

2602 

2672 

2742 

2812 

2882 

2952 

3022 

70 

621 

3092 

3162 

3231 

3301 

3371 

3441 

3511 

3581 

3651 

3721 

70 

'  622 

3790 

3860 

3930 

4000 

4070 

4139 

4209 

4279 

4349 

4418 

70 

623 

4488 

4558 

4627 

4697 

4767 

4836 

4906 

4976 

5045 

5115 

70 

624 

5185 

5254 

5324 

5393 

5463 

5532 

5602 

5672 

5741 

5811 

70 

625 

5880 

5949 

6019 

6088 

6158 

6227 

6297 

6366 

6436 

6505 

69 

626 

6574 

6644 

6713 

6782 

6852 

6921 

6990 

7060 

7129 

7198 

69 

627 

7268 

7337 

7406 

7475 

7545 

7614 

7683 

7752 

7821 

7890 

69 

628 

7960 

8029 

8098 

8167 

8236 

8305 

8374 

8443 

8513 

8582 

69 

629 

8651 

8720 

8789 

8858 

8927 

8996 

9065 

9134 

9203 

9272 

69 

630 

799341 

9409 

9478 

9547 

9616 

9685 

9754 

9823 

9892 

9961 

69 

631 

800029 

0098 

0167 

0236 

0305 

0373 

0442 

0511 

0580 

0648 

69 

632 

0717 

0786 

0854 

0923 

0992 

1061 

1129 

1198 

1266 

1335 

69 

633 

1404 

1472 

1541 

1609 

1678 

1747 

1815 

1884 

1952 

2021 

69 

634 

2089 

2158 

2226 

2295 

2363 

2432 

2500 

2568 

2637 

2705 

69 

635 

2774 

2842 

2910 

2979 

3047 

3116 

3184 

3252 

3321 

3389 

68 

636 

3457 

3525 

3594 

3662 

•3730 

3798 

3867 

3935 

4003 

4071 

68 

637 

4139 

4208 

4276 

4344 

4412 

4480 

4548 

4616 

4685 

4753 

68 

638 

4821 

4889 

4957 

5025 

5093 

5161 

5229 

5297 

5365 

5433 

68 

639 

5501 

5569 

5637 

5705 

5773 

5841 

5908 

5976 

6044 

6112 

68 

640 

806180 

6248 

6316 

6384 

6451 

6519 

6587 

6655 

6723 

6790 

68 

641 

6858 

6926 

6994 

7061 

7129 

7197 

7264 

7332 

7400 

7467 

68 

642 

7535 

7603 

7670 

7738 

7806 

7873 

7941 

8008 

8076 

8143 

68 

643 

8211 

8279 

8346 

8414 

8481 

8549 

8616 

8684 

8751 

8818 

67 

644 

8886 

8953 

9021 

9088 

9156 

9223 

9290 

9358 

9425 

9492 

67 

645 

9560 

9627 

9694 

9762 

9829 

9896 

9964 

**31 

**9S 

*165 

67 

646 

810233 

0300 

0367 

0434 

0501 

0569 

0636 

0703 

0770 

0837 

67 

647 

0904 

0971 

1039 

1106 

1173 

1240 

1307 

1374 

1441 

1508 

67 

648 

1575 

1642 

1709 

1776 

1843 

1910 

1977 

2044 

2111 

2178 

67 

649 

2245 

2312 

2379 

2445 

2512 

2579 

2646 

2713 

2780 

2847 

67 

N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

D. 

58 


TABLE  XXIX  (CONTINUED) 


N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

D. 

650 

812913 

2980 

3047 

3114 

3181 

3247 

3314 

3381 

3448 

3514 

67 

651 

3581 

3648 

3714 

3781 

3848 

3914 

3981 

4048 

4114 

4181 

67 

652 

4248 

4314 

4381 

4447 

4514 

4581 

4647 

4714 

4780 

4847 

67 

653 

4913 

4980 

5046 

5113 

5179 

5246 

5312 

5378 

5445 

5511 

66 

654 

5578 

5644 

5711 

5777 

5843 

5910 

5976 

6042 

6109 

6175 

66 

655 

6241 

6308 

6374 

6440 

6506 

6573 

6639 

6705 

6771 

6838 

66 

656 

6904 

6970 

7036 

7102 

7169 

7235 

7301 

7367 

7433 

7499 

66 

657 

7565 

7631 

7698 

7764 

7830 

7896 

7962 

8028 

8094 

8160 

66 

658 

8226 

8292 

8358 

8424 

8490 

8556 

8622 

8688 

8754 

8820 

66 

659 

8885 

8951 

9017 

9083 

9149 

9215 

9281 

9346 

9412 

9478 

66 

660 

819544 

9610 

9676 

9741 

9807 

9873 

9939 

##*4 

**70 

*136 

66 

661 

820201 

0267 

0333 

0399 

0464 

0530 

0595 

0661 

0727 

0792 

66 

662 

0858 

0924 

0989 

1055 

1120 

1186 

1251 

1317 

1382 

1448 

66 

663 

1514 

1579 

1645 

1710 

1775 

1841 

1906 

1972 

2037 

2103 

65 

664 

2168 

2233 

2299 

2364 

2430 

2495 

2560 

2626 

2691 

2756 

65 

665 

2822 

2887 

2952 

3018 

3083 

3148 

3213 

3279 

3344 

3409 

65 

666 

3474 

3539 

3605 

3670 

3735 

3SOO 

3865 

3930 

3996 

4061 

65 

667 

4126 

4191 

4256 

4321 

4386 

4451 

4516 

4581 

4646 

4711 

65 

668 

4776 

4841 

4906 

4971 

5036 

5101 

5166 

5231 

5296 

5361 

65 

669 

5426 

5491 

5556 

5621 

5686 

5751 

5815 

5880 

5945 

6010 

65 

670 

826075 

6140 

6204 

6269 

6334 

6399 

6464 

6528 

6593 

6658 

65 

671 

6723 

6787 

6852 

6917 

6981 

7046 

7111 

7175 

7240 

7305 

65 

672 

7369 

7434 

7499 

7563 

7628 

7692 

7757 

7821 

7SS6 

7951 

65 

673 

8015 

8080 

8144 

8209 

8273 

833S 

8402 

8467 

8531 

8595 

64 

674 

8660 

8724 

8789 

SS53 

8918 

S9S2 

9046 

9111 

9175 

9239 

64 

675 

9304 

9368 

9432 

9497 

9561 

9625 

9690 

9754 

9S18 

9882 

64 

676 

9947 

##H 

**75 

*139 

*204 

*26S 

*332 

*396 

*460 

*525 

64 

677 

830589 

0653 

0717 

0781 

0845 

0909 

0973 

1037 

1102 

1166 

64 

678 

1230 

1294 

1358 

1422 

I486 

1550 

1614 

1678 

1742 

1805 

64 

679 

1870 

1934 

1998 

2062 

2126 

2189 

2253 

2317 

2381 

2445 

64 

680 

832509 

2573 

2637 

2700 

2764 

2828 

2892 

2956 

3020 

3083 

64 

681 

3147 

3211 

3275 

3338 

3402 

3466 

3530 

3593 

3657 

3721 

64 

682 

3784 

3848 

3912 

3975 

4039 

4103 

4166 

4230 

4294 

4357 

64 

683 

4421 

4484 

4548 

4611 

4675 

4739 

4802 

4866 

4929 

4993 

64 

684 

5056 

5120 

5183 

5247 

5310 

5373 

5437 

5500 

5564 

5627 

63 

685 

5691 

5754 

5817 

5881 

5944 

6007 

6071 

6134 

6197 

6261 

63 

686 

6324 

6387 

6451 

6514 

6577 

6641 

6704 

6767 

6830 

6894 

63 

687 

6957 

7020 

7083 

7146 

7210 

7273 

7336 

7399 

7462 

7525 

63 

688 

7588 

7652 

7715 

7778 

7841 

7904 

7967 

8030 

8093 

8156 

63 

689 

8219 

8282 

8345 

8408 

8471 

8534 

8597 

8660 

8723 

8786 

63 

690 

838849 

8912 

8975 

9038 

9101 

9164 

9227 

9289 

9352 

9415 

63 

691 

9478 

9541 

9604 

9667 

9729 

9792 

9855 

9918 

9981 

**43 

63 

692 

840106 

0169 

0232 

0294 

0357 

0420 

0482 

0545 

0608 

0671 

63 

693 

0733 

0796 

0859 

0921 

0984 

1046 

1109 

1172 

1234 

1297 

63 

694 

1359 

1422 

1485 

1547 

1610 

1672 

1735 

1797 

1860 

1922 

63 

695 

1985 

2047 

2110 

2172 

2235 

2297 

2360 

2422 

2484 

2547 

62 

696 

2609 

2672 

2734 

2796 

2859 

2921 

2983 

3046 

3108 

3170 

62 

697 

3233 

3295 

3357 

3420 

3482 

3544 

3606 

3669 

3731 

3793 

62 

698 

3855 

3918 

3980 

4042 

4104 

4166 

4229 

4291 

4353 

4415 

62 

699 

4477 

4539 

4601 

4664 

4726 

4788 

4850 

4912 

4974 

5036 

62 

N. 

0 

1 

2 

3 

4 

5     6 

7 

8 

9 

D. 

TABLE   XXIX  (CONTINUED) 


59 


N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

D. 

700 

845098 

5160 

5222 

5284 

5346 

5408 

5470 

5532 

5594 

5656 

62 

701 

5718 

5780 

5842 

5904 

5966 

6028 

6090 

6151 

6213 

6275 

62 

702 

6337 

6399 

6461 

6523 

6585 

6646 

6708 

6770 

6832 

6894 

62 

703 

6955 

7017 

7079 

7141 

7202 

7264 

7326 

7388 

7449 

7511 

62 

704 

7573 

7634 

7696 

7758 

7819 

7881 

7943 

8004 

8066 

8128 

62 

705 

8189 

8251 

8312 

8374 

8435 

8497 

8559 

8620 

8682 

8743 

62 

706 

8805 

8866 

8928 

8989 

9051 

9112 

9174 

9235 

9297 

9358 

61 

707 

9419 

9481 

9542 

9604 

9665 

9726 

9788 

9849 

9911 

9972 

61 

70S 

850033 

0095 

0156 

0217 

0279 

0340 

0401 

0462 

0524 

0585 

61 

709 

0646 

0707 

0769 

OS30 

0891 

0952 

1014 

1075 

1136 

1197 

61 

710 

851258 

1320 

1381 

1442 

1503 

1564 

1625 

1686 

1747 

1809 

61 

711 

1870 

1931 

1992 

2053 

2114 

2175 

2236 

2297 

2358 

2419 

61 

712 

2480 

2541 

2602 

2663 

2724 

2785 

2846 

2907 

2968 

3029 

61 

713 

3090 

3150 

3211 

3272 

3333 

3394 

3455 

3516 

3577 

3637 

61 

714 

3698 

3759 

3820 

3881 

3941 

4002 

4063 

4124 

4185 

4245 

61 

715 

4306 

4367 

4428 

4488 

4549 

4610 

4670 

4731 

4792 

4852 

61 

716 

4913 

4974 

5034 

5095 

5156 

5216 

5277 

5337 

5398 

5459 

61 

717 

5519 

5580 

5640 

5701 

5761 

5822 

5882 

5943 

6003 

6064 

61 

718 

6124 

61S5 

6245 

6306 

6366 

6427 

6487 

6548 

6608 

6668 

60 

719 

6729* 

6789 

6850 

6910 

6970 

7031 

7091 

7152 

7212 

7272 

60 

720 

857332 

7393 

7453 

7513 

7574 

7634 

7694 

7755 

7815 

7875 

60 

721 

7935 

7995 

8056 

8116 

8176 

8236 

8297 

8357 

8417 

8477 

60 

722 

8537 

8597 

8657 

8718 

8778 

8838 

8898 

8958 

9018 

9078 

60 

723 

9138 

9198 

9258 

9318 

9379 

9439 

9499 

9559 

9619 

9679 

60 

724 

9739 

9799 

9859 

9918 

9978 

**3S 

**9S 

*158 

*21S 

*278 

60 

725 

860338 

0398 

0458 

0518 

0578 

0637 

0697 

0757 

0817 

0877 

60 

726 

0937 

0996 

1056 

1116 

1176 

1236 

1295 

1355 

1415 

1475 

60 

727 

1534 

1594 

1654 

1714 

1773 

1833 

1893 

1952 

2012 

2072 

60 

728 

2131 

2191 

2251 

2310 

2370 

2430 

2489 

2549 

2608 

2668 

60 

729 

2728 

2787 

2847 

2906 

2966 

3025 

3085 

3144 

3204 

3263 

60 

730 

863323 

3382 

3442 

3501 

3561 

3620 

3680 

3739 

3799 

3858 

59 

731 

3917 

3977 

4036 

4096 

4155 

4214 

4274 

4333 

4392 

4452 

59 

732 

4511 

4570 

4630 

4689 

4748 

4808 

4867 

4926 

4985 

5045 

59 

733 

5104 

5163 

5222 

5282 

5341 

5400 

5459 

5519 

5578 

5637 

59 

734 

5696 

5755 

5814 

5874 

5933 

5992 

6051 

6110 

6169 

6228 

59 

735 

6287 

6346 

6405 

6465 

6524 

6583 

6642 

6701 

6760 

6819 

59 

736 

6878 

6937 

6996 

7055 

7114 

7173 

7232 

7291 

7350 

7409 

59 

737 

7467 

7526 

7585 

7644 

7703 

7762 

7821 

7880 

7939 

7998 

59 

738 

8056 

8115 

8174 

8233 

8292 

8350 

84  09 

8468 

8527 

8586 

59 

739 

8644 

8703 

8762 

8821 

8879 

8938 

8997 

9056 

9114 

9173 

59 

740 

869232 

9290 

9349 

9408 

9466 

9525 

9584 

9642 

9701 

9760 

59 

741 

9818 

9877 

9935 

9994 

**53 

*111 

*170 

*228 

*287 

*345 

59 

742 

870404 

0462 

0521 

0579 

0638 

0696 

0755 

0813 

0872 

0930 

58 

743 

0989 

1047 

1106 

1164 

1223 

1281 

1339 

1398 

1456 

1515 

58 

744 

1573 

1631 

1690 

1748 

1806 

1865 

1923 

1981 

2040 

2098 

58 

745 

2156 

2215 

2273 

2331 

2389 

2448 

2506 

2564 

2622 

2681 

58 

746 

2739 

2797 

2855 

2913 

2972 

3030 

3088 

3146 

3204 

3262 

58 

747 

3321 

3379 

3437 

3495 

3553 

3611 

3669 

3727 

3785 

3844 

58 

748 

3902 

3960 

4018 

4076 

4134 

4192 

4250 

4308 

4366 

4424 

58 

749 

4482 

4540 

4598 

4656 

4714 

4772 

4830 

4888 

4945 

5003 

58 

N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

D. 

60 


TABLE  XXIX   (CONTINUED) 


N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

D. 

750 

875061 

5119 

5177 

5235 

5293 

5351 

5409 

5466 

5524 

5582 

58 

751 

5640 

5698 

5756 

5813 

5871 

5929 

5987 

6045 

6102 

6160 

58 

752 

6218 

6276 

6333 

6391 

6449 

6507 

6564 

6622 

6680 

6737 

58 

753 

6795 

6S53 

6910 

6968 

7026 

7083 

7141 

7199 

7256 

7314 

58 

754 

7371 

7429 

7487 

7544 

7602 

7659 

7717 

7774 

7832 

7889 

58 

755 

7947 

8004 

8062 

8119 

8177 

8234 

8292 

8349 

8407 

8464 

57 

756 

8522 

8579 

8637 

8694 

8752 

8809 

8866 

8924 

8981 

9039 

57 

757 

9096 

9153 

9211 

9268 

9325 

9383 

9440 

9497 

9555 

9612 

57 

758 

9669 

9726 

9784 

9841 

9898 

9956 

**13 

**70 

*127 

*185 

57 

759 

880242 

0299 

0356 

0413 

0471 

0528 

0585 

0642 

0699 

0756 

57 

760 

880814 

0871 

0928 

0985 

1042 

1099 

1156 

1213 

1271 

1328 

57 

761 

1385 

1442 

1499 

1556 

1613 

1670 

1727 

1784 

1841 

1898 

57 

762 

1955 

2012 

2069 

2126 

21S3 

2240 

2297 

2354 

2411 

2468 

57 

763 

2525 

2581 

2638 

2695 

2752 

2809 

2866 

2923 

2980 

3037 

57 

764 

3093 

3150 

3207 

3264 

3321 

3377 

3434 

3491 

3548 

3605 

57 

765 

3661 

3718 

3775 

3832 

3SS8 

3945 

4002 

4059 

4115 

4172 

57 

766 

4229 

4285 

4342 

4399 

4455 

4512 

4569 

4625 

4682 

4739 

57 

767 

4795 

4852 

4909 

4965 

5022 

5078 

5135 

5192 

5248 

5305 

57 

768 

5361 

5418 

5474 

5531 

5587 

5644 

5700 

5757 

5813 

5870 

57 

769 

5926 

5983 

6039 

6096 

6152 

6209 

6265 

6321 

63  78 

6434 

56 

770 

8S6491 

6547 

6604 

6660 

6716 

6773 

6829 

6885 

6942 

6998 

56 

771 

7054 

7111 

7167 

7223 

7280 

7336 

7392 

7449 

7505 

7561 

56 

772 

7617 

7674 

7730 

7786 

7842 

7898 

7955 

8011 

8067 

8123 

56 

.773 

8179 

8236 

8292 

8348 

8404 

8460 

8516 

8573 

8629 

8685 

56 

774 

8741 

8797 

8853 

8909 

8965 

9021 

9077 

9134 

9190 

9246 

56 

775 

9302 

9358 

9414 

9470 

9526 

9582 

9638 

9694 

9750 

9806 

56 

776 

9862 

9918 

9974 

**30 

**S6 

*141 

*197 

*253 

*309 

*365 

56 

777 

890421 

0477 

0533 

0589 

0645 

0700 

0756 

0812 

0868 

0924 

56 

778 

0980 

1035 

1091 

1147 

1203 

1259 

1314 

1370 

1426 

1482 

56 

779 

1537 

1593 

1649 

1705 

1760 

1816 

1872 

1928 

1983 

2039 

56 

780 

892095 

2150 

2206 

2262 

2317 

2373 

2429 

2484 

2540 

2595 

56 

781 

2651 

2707 

2762 

2818 

2873 

2929 

2985 

3040 

3096 

3151 

56 

782 

3207 

3262 

3318 

3373 

3429 

3484 

3540 

3595 

3651 

3706 

56 

783 

3762 

3817 

3873 

3928 

3984 

4039 

4094 

4150 

4205 

4261 

55 

784 

4316 

4371 

4427 

4482 

4538 

4593 

4648 

4704 

4759 

4814 

55 

785 

4870 

4925 

4980 

5036 

5091 

5146 

5201 

5257 

5312 

5367 

55 

786 

5423 

5478 

5533 

5588 

5644 

5699 

5754 

5809 

5864 

5920 

55 

787 

5975 

6030 

6085 

6140 

6195 

6251 

6306 

6361 

6416 

6471 

55 

788 

6526 

6581 

6636 

6692 

6747 

6802 

6857 

6912 

6967 

7022 

55 

789 

7077 

7132 

7187 

7242 

7297 

7352 

7407 

7462 

7517 

7572 

55 

790 

897627 

7682 

7737 

7792 

7847 

7902 

7957 

8012 

8067 

8122 

55 

791 

8176 

8231 

8286 

8341 

8396 

8451 

8506 

8561 

8615 

8670 

55 

792 

8725 

8780 

8835 

8890 

8944 

8999 

9054 

9109 

9164 

9218 

55 

793 

9273 

9328 

9383 

9437 

9492 

9547 

9602 

9656 

9711 

9766 

55 

794 

9821 

9875 

9930 

9985 

**39 

**94 

*149 

*203 

*258 

*312 

55 

795 

900367 

0422 

0476 

0531 

0586 

0640 

0695 

0749 

0804 

0859 

55 

796 

0913 

0968 

1022 

1077 

1131 

1186 

1240 

1295 

1349 

1404 

55 

797 

1458 

1513 

1567 

1622 

1676 

1731 

1785 

1840 

1894 

1948 

54 

798 

2003 

2057 

2112 

2166 

2221 

2275 

2329 

2384 

2438 

2492 

54 

799 

2547 

2601 

2655 

2710 

2764 

2818 

2873 

2927 

2981 

3036 

54 

N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

D. 

TABLE  XXIX  (CONTINUED) 


61 


N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

D. 

800 

903090 

3144 

3199 

3253 

3307 

3361 

3416 

3470 

3524 

3578 

54 

801 

3633 

3687 

3741 

3795 

3849 

3904 

3958 

4012 

4066 

4120 

54 

802 

4174 

4229 

4283 

4337 

4391 

4445 

4499 

4553 

4607 

4661 

54 

803 

4716 

4770 

4824 

4878 

4932 

4986 

5040 

5094 

5148 

5202 

54 

804 

5256 

5310 

5364 

5418 

5472 

5526 

5580 

5634 

5688 

5742 

54 

805 

5796 

5850 

5904 

5958 

6012 

6066 

6119 

6173 

6227 

6281 

54 

806 

6335 

6389 

6443 

6497 

6551 

6604 

6658 

6712 

6766 

6820 

54 

807 

6874 

6927 

6981 

7035 

7089 

7143 

7196 

7250 

7304 

7358 

54 

808 

7411 

7465 

7519 

7573 

7626 

7680 

7734 

7787 

7841 

7895 

54 

809 

7949 

8002 

8056 

8110 

8163 

8217 

8270 

8324 

8378 

8431 

54 

810 

908485 

8539 

8592 

8646 

8699 

8753 

8807 

8860 

8914 

8967 

54 

811 

9021 

9074 

9128 

9181 

9235 

9289 

9342 

9396 

9449 

9503 

54 

812 

9556 

9610 

9663 

9716 

9770 

9823 

9877 

9930 

9984 

**37 

53 

813 

910091 

0144 

0197 

0251 

0304 

0358 

0411 

0464 

0518 

0571 

53 

814 

0624 

0678 

0731 

0784 

0838 

0891 

0944 

0998 

1051 

1104 

53 

815 

1158 

1211 

1264 

1317 

1371 

1424 

1477 

1530 

1584 

1637 

53 

816 

1690 

1743 

1797 

1850 

1903 

1956 

2009 

2063 

2116 

2169 

53 

817 

2222 

2275 

2328 

2381 

2435 

2488 

2541 

2594 

2647 

2700 

53 

818 

2753 

2806 

2859 

2913 

2966 

3019 

3072 

3125 

3178 

3231 

53 

819 

3284 

3337 

3390 

3443 

3496 

3549 

3602 

3655 

3708 

3761 

53 

820 

913814 

3867 

3920 

3973 

4026 

4079 

4132 

4184 

4237 

4290 

53 

821 

4343 

4396 

4449 

4502 

4555 

4608 

4660 

4713 

4766 

4819 

53 

822 

4872 

4925 

4977 

5030 

5083 

5136 

5189 

5241 

5294 

5347 

53 

823 

5400 

5453 

5505 

5558 

5611 

5664 

5716 

5769 

5822 

5875 

53 

824 

5927 

5980 

6033 

6085 

6138 

6191 

6243 

6296 

6349 

6401 

53 

825 

6454 

6507 

6559 

6612 

6664 

6717 

6770 

6822 

6875 

6927 

53 

826 

6980 

7033 

7085 

7138 

7190 

7243 

7295 

7348 

7400 

7453 

53 

827 

7506 

7558 

7611 

7663 

7716 

7768 

7820 

7873 

7925 

7978 

52 

828 

8030 

8083 

8135 

8188 

82-40 

8293 

8345 

8397 

8450 

8502 

52 

829 

8555 

8607 

8659 

8712 

8764 

S816 

8869 

8921 

8973 

9026 

52 

830 

919078 

9130 

9183 

9235 

9287 

9340 

9392 

9444 

9496 

9549 

52 

831 

9601 

9653 

9706 

9758 

9810 

9862 

9914 

9967 

**19 

**71 

52 

832 

920123 

0176 

0228 

0280 

0332 

0384 

0436 

0489 

0541 

0593 

52 

833 

0645 

0697 

0749 

0801 

0853 

0906 

0958 

1010 

1062 

1114 

52 

834 

1166 

1218 

1270 

1322 

1374 

1426 

1478 

1530 

1582 

1634 

52 

835 

1686 

1738 

1790 

1842 

1894 

1946 

1998 

2050 

2102 

2154 

52 

836 

2206 

2258 

2310 

2362 

2414 

2466 

2518 

2570 

2622 

2674 

52 

837 

2725 

2777 

2829 

2881 

2933 

2985 

3037 

3089 

3140 

3192 

52 

838 

3244 

3296 

3348 

3399 

3451 

3503 

3555 

3607 

3658 

3710 

52 

839 

3762 

3814 

3865 

3917 

3969 

4021 

4072 

4124 

4176 

4228 

52 

840 

924279 

4331 

4383 

4434 

4486 

4538 

4589 

4641 

4693 

4744 

52 

841 

4796 

4848 

4899 

4951 

5003 

5054 

5106 

5157 

5209 

5261 

52 

842 

5312 

5364 

5415 

5467 

5518 

5570 

5621 

5673 

5725 

5776 

52 

843 

5828 

5879 

5931 

5982 

6034 

6085 

6137 

6188 

6240 

6291 

51 

844 

6342 

6394 

6445 

6497 

6548 

6600 

6651 

6702 

6754 

6805 

51 

845 

6857 

6908 

6959 

7011 

7062 

7114 

7165 

7216 

7268 

7319 

51 

846 

7370 

7422 

7473 

7524 

7576 

7627 

7678 

7730 

7781 

7832 

51 

847 

7883 

7935 

79S6 

8037 

8088 

8140 

9191 

8242 

8293 

8345 

51 

848 

8396 

8447 

8498 

8549 

8601 

8652 

8703 

8754 

8805 

8857 

51 

849 

8908 

8959 

9010 

9061 

9112 

9163 

9215 

9266 

9317 

9368 

51 

N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

D. 

62 


TABLE  XXIX  (COXTIXUED) 


N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

D. 

850 

929419 

9470 

9521 

9572 

9623 

9674 

9725 

9776 

9827 

9879 

51 

851 

9930 

9981 

**32 

**S3 

*134 

*185 

*236 

*287 

*338 

*389 

51 

852 

930440 

0491 

0542 

0592 

0643 

0694 

0745 

0796 

0847 

0898 

51 

853 

0949 

1000 

1051 

1102 

1153 

1204 

1254 

1305 

1356 

1407 

51 

854 

1458 

1509 

1560 

1610 

1661 

1712 

1763 

1814 

1865 

1915 

51 

855 

1966 

2017 

2068 

2118 

2169 

2220 

2271 

2322 

2372 

2423 

51 

856 

2474 

2524 

2575 

2626 

2677 

2727 

2778 

2829 

2879 

2930 

51 

857 

2981 

3031 

3082 

3133 

3183 

3234 

3285 

3335 

3386 

3437 

51 

858 

34S7 

3538 

3589 

3639 

3690 

3740 

3791 

3841 

3892 

3943 

51 

859 

3993 

4044 

4094 

4145 

4195 

4246 

4296 

4347 

4397 

4448 

51 

860 

934498 

4549 

4599 

4650 

4700 

4751 

4801 

4852 

4902 

4953 

50 

861 

5003 

5054 

5104 

5154 

5205 

5255 

5306 

5356 

5406 

5457 

50 

862 

5507 

5558 

5608 

5658 

5709 

5759 

5809 

5860 

5910 

5960 

50 

863 

6011 

6061 

6111 

6162 

6212 

6262 

6313 

6363 

6413 

6463 

50 

864 

6514 

6564 

6614 

6665 

6715 

6765 

6815 

6865 

6916 

6966 

50 

865 

7016 

7066 

7117 

7167 

7217 

7267 

7317 

7367 

7418 

7468 

50 

866 

7518 

7568 

7618 

7668 

7718 

7769 

7819 

7869 

7919 

7969 

50 

867 

8019 

8069 

8119 

8169 

8219 

8269 

8320 

8370 

8420 

8470 

50 

868 

8520 

8570 

8620 

8670 

8720 

8770 

8820 

8870 

8920 

8970 

50 

869 

9020 

9070 

9120 

9170 

9220 

9270 

9320 

9369 

9419 

9469 

50 

870 

939519 

9569 

9619 

9669 

9719 

9769 

9819 

9869 

9918 

9968 

50 

871 

940018 

006S 

0118 

0168 

0218 

0267 

0317 

0367 

0417 

0467 

50 

872 

0516 

0566 

0616 

0666 

0716 

0765 

0815 

0865 

0915 

0964 

50 

873 

1014 

1064 

1114 

1163 

1213 

1263 

1313 

1362 

1412 

1462 

50 

874 

1511 

1561 

1611 

1660 

1710 

1760 

1809 

1859 

1909 

1958 

50 

875 

2008 

2058 

2107 

2157 

2207 

2256 

2306 

2355 

2405 

2455 

50 

876 

2504 

2554 

2603 

2653 

2702 

2752 

2801 

2851 

2901 

2950 

50 

877 

3000 

3049 

3099 

3148 

3198 

3247 

3297 

3346 

3396 

3445 

49 

878 

3495 

3544 

3593 

3643 

3692 

3742 

3791 

3841 

3890 

3939 

49 

879 

3989 

4038 

4088 

4137 

4186 

4236 

4285 

4335 

4384 

4433 

49 

880 

944483 

4532 

4581 

4631 

4680 

4729 

4779 

4828 

4877 

4927 

49 

881 

4976 

5025 

5074 

5124 

5173 

5222 

5272 

5321 

5370 

5419 

49 

882 

5469 

5518 

5567 

5616 

5665 

5715 

5764 

5813 

5862 

5912 

49 

883 

5961 

6010 

6059 

6108 

6157 

6207 

6256 

6305 

6354 

6403 

49 

884 

6452 

6501 

6551 

6600 

6649 

6698 

6747 

6796 

6845 

6894 

49 

885 

6943 

6992 

7041 

7090 

7140 

7189 

7238 

7287 

7336 

7385 

49 

886 

7434 

7483 

7532 

7581 

7630 

7679 

7728 

7777 

7826 

7875 

49 

887 

7924. 

7973 

8022 

8070 

8119 

8168 

8217 

8366 

8315 

8364 

49 

888 

8413 

8462 

8511 

8560 

8609 

8657 

8706 

8755 

8804 

8853 

49 

889 

8902 

8951 

8999 

9048 

9097 

9146 

9195 

9244 

9292 

9341 

49 

890 

949390 

9439 

9488 

9536 

9585 

9634 

9683 

9731 

9780 

9829 

49 

891 

9878 

9926 

9975 

**24 

**73 

*121 

*170 

*219 

*267 

*316 

49 

892 

950365 

0414 

0462 

0511 

0560 

0608 

0657 

0706 

0754 

0803 

49 

893 

0851 

0900 

0949 

0997 

1046 

1095 

1143 

1192 

1240 

1289 

49 

894 

1338 

1386 

1435 

1483 

1532 

1580 

1629 

1677 

1726 

1775 

49 

895 

1823 

1872 

1920 

1969 

2017 

2066 

2114 

2163 

2211 

2260 

48 

896 

2308 

2356 

2405 

2453 

2502 

2550 

2599 

2647 

2696 

2744 

48 

897 

2792 

2841 

2889 

2938 

2986 

3034 

3083 

3131 

3180 

3228 

48 

898 

3276 

3325 

3373 

3421 

3470 

3518 

3566 

3615 

3663 

3711 

48 

899 

3760 

3808 

3856 

3905 

3953 

4001 

4049 

4098 

4146 

4194 

48 

W. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

D. 

TABLE  XXIX  (CONTINUED) 


63 


N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

D. 

900 

954243 

4291 

4339 

4387 

4435 

4484 

4532 

4580 

4628 

4677 

48 

901 

4725 

4773 

4821 

4869 

4918 

4966 

5014 

5062 

5110 

5158 

48 

902 

5207 

5255 

5303 

5351 

5399 

5447 

5495 

5543 

5592 

5640 

48 

903 

5688 

5736 

5784 

5832 

5880 

5928 

5976 

6024 

6072 

6120 

48 

904 

6168 

6216 

6265 

6313 

6361 

6409 

6457 

6505 

6553 

6601 

48 

905 

6649 

6697 

6745 

6793 

6840 

6888 

6936 

6984 

7032 

7080 

48 

906 

7128 

7176 

7224 

7272 

7320 

7368 

7416 

7464 

7512 

7559 

48 

907 

7607 

7655 

7703 

7751 

7799 

7847 

7894 

7942 

7990 

8038 

48 

908 

8086 

8134 

8181 

8229 

8277 

8325 

8373 

8421 

8468 

8516 

48 

909 

8564 

8612 

8659 

8707 

8755 

8803 

8850 

8898 

8946 

8994 

48 

910 

959041 

9089 

9137 

9185 

9232 

9280 

9328 

9375 

9423 

9471 

48 

911 

9518 

9566 

9614 

9661 

9709 

9757 

9804 

9852 

9900 

9947 

48 

912 

9995 

**42 

**90 

*13S 

*185 

*233 

*2SO 

*32S 

*376 

*423 

48 

913 

960471 

0518 

0566 

0613 

0661 

0709 

0756 

0804 

0851 

0899 

48 

914 

0946 

0994 

1041 

1089 

1136 

1184 

1231 

1279 

1326 

1374 

47 

915 

1421 

1469 

1516 

1563 

1611 

1658 

1706 

1753 

1801 

1848 

47 

916 

1895 

1943 

1990 

2038 

2085 

2132 

2180 

2227 

2275 

2322 

47 

917 

2369 

2417 

2464 

2511 

2559 

2606 

2653 

2701 

2748 

2795 

47 

918 

2843 

2890 

2937 

2985 

3032 

3079 

3126 

3174 

3221 

3268 

47 

919 

3316 

3363 

3410 

3457 

3504 

3552 

3599 

3646 

3693 

3741 

47 

920 

963788 

3835 

3882 

3929 

3977 

4024 

4071 

4118 

4165 

4212 

47 

921 

4260 

4307 

4354 

4401 

4448 

4495 

4542 

4590 

4637 

4684 

47 

922 

4731 

4778 

4825 

4872 

4919 

4966 

5013 

5061 

5108 

5155 

47 

923 

5202 

5249 

5296 

5343 

5390 

5437 

5484 

5531 

5578 

5625 

47 

924 

5672 

5719 

5766 

5813 

5860 

5907 

5954 

6001 

6048 

6095 

47 

925 

6142 

6189 

6236 

6283 

6329 

6376 

6423 

6470 

6517 

6564 

47 

926 

6611 

6658 

6705 

6752 

6799 

6845 

6892 

6939 

6986 

7033 

47 

927 

7080 

7127 

7173 

7220 

7267 

7314 

7361 

7408 

7454 

7501 

47 

928 

7548 

7595 

7642 

7688 

7735 

7782 

7829 

7S75 

7922 

7969 

47 

929 

8016 

8062 

8109 

8156 

8203 

8249 

8296 

8343 

8390 

8436 

.47 

930 

968483 

8530 

8576 

8623 

8670 

8716 

8763 

8810 

8856 

8903 

47 

931 

8950 

8996 

9043 

9090 

9136 

9183 

9229 

9276 

9323 

9369 

47 

932 

9416 

9463 

9509 

9556 

9602 

9649 

9695 

9742 

9789 

9835 

47 

933 

9882 

9928 

9975 

*#21 

**6S 

#114 

*161 

*207 

*254 

*300 

47 

934 

970347 

0393 

0440 

0486 

0533 

0579 

0626 

0672 

0719 

0765 

46 

935 

0812 

0858 

0904 

0951 

0997 

1044 

1090 

1137 

1183 

1229 

46 

936 

1276 

1322 

1369 

1415 

1461 

1508 

1554 

1601 

1647 

1693 

46 

937 

1740 

1786 

1832 

1879 

1925 

1971 

2018 

2064 

2110 

2157 

46 

938 

2203 

2249 

2295 

2342 

2388 

2434 

2481 

2527 

2573 

2619 

46 

939 

2666 

2712 

2758 

2804 

2851 

2897 

2943 

2989 

3035 

3082 

46 

940 

973128 

3174 

3220 

3266 

3313 

3359 

3405 

3451 

3497 

3543 

46 

941 

3590 

3636 

3682 

3728 

3774 

3820 

3866 

3913 

3959 

4005 

46 

942 

4051 

4097 

4143 

4189 

4235 

4281 

4327 

4374 

4420 

4466 

46 

943 

4512 

4558 

4604 

4650 

4696 

4742 

4788 

4834 

4880 

4926 

46 

944 

4972 

5018 

5064 

5110 

5156 

5202 

5248 

5294 

5340 

5386 

46 

945 

5432 

5478 

5524 

5570 

5616 

5662 

5707 

5753 

5799 

5845 

46 

946 

5891 

5937 

5983 

6029 

6075 

6121 

6167 

6212 

6258 

6304 

46 

947 

6350 

6396 

6442 

6488 

6533 

6579 

6625 

6671 

6717 

6763 

46 

948 

6808 

6854 

6900 

6946 

6992 

7037 

7083 

7129 

7175 

7220 

46 

949 

7266 

7312 

7358 

7403 

7449 

7495 

7541 

7586 

7632 

7678 

46 

N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

D. 

TABLE  XXIX  (CONTINUED) 


N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

D. 

950 

977724 

7769 

7815 

7861 

7906 

7952 

7998 

8043 

8089 

8135 

46 

951 

8181 

8226 

8272 

8317 

8363 

8409 

8454 

8500 

8546 

8591 

46 

952 

8637 

8683 

8728 

8774 

8819 

8865 

8911 

8956 

9002 

9047 

46 

953 

9093 

9138 

9184 

9230 

9275 

9321 

9366 

9412 

9457 

9503 

46 

954 

9548 

9594 

9639 

9685 

9730 

9776 

9821 

9867 

9912 

9958 

46 

955 

980003 

0049 

0094 

0140 

0185 

0231 

0276 

0322 

0367 

0412 

45 

956 

0458 

0503 

0549 

0594 

0640 

0685 

0730 

0776 

0821 

0867 

45 

957 

0912 

0957 

1003 

104S 

1093 

1139 

1184 

1229 

1275 

1320 

45 

958 

1365 

1411 

1456 

1501 

1547 

1592 

1637 

1683 

1728 

1773 

45 

959 

1819 

1864 

1909 

1954 

2000 

2045 

2090 

2135 

2181 

2226 

45 

960 

982271 

2316 

2362 

2407 

2452 

2497 

2543 

2588 

2633 

2678 

45 

961 

2723 

2769 

2814 

2859 

2904 

2949 

2994 

3040 

3085 

3130 

45 

962 

3175 

3220 

3265 

3310 

3356 

3401 

3446 

3491 

3536 

3581 

45 

963 

3626 

3671 

3716 

3762 

3807 

3852 

3897 

3942 

3987 

4032 

45 

964 

4077 

4122 

4167 

4212 

4257 

4302 

4347 

4392 

4437 

4482 

45 

965 

4527 

4572 

4617 

4662 

4707 

4752 

4797 

4842 

4887 

4932 

45 

966 

4977 

5022 

5067 

5112 

5157 

5202 

5247 

5292 

5337 

5382 

45 

967 

5426 

5471 

5516 

5561 

5606 

5651 

5696 

5741 

5786 

5830 

45 

968 

5875 

5920 

5965 

6010 

6055 

6100 

6144 

6189 

6234 

6279 

45 

969 

6324 

6369 

6413 

6458 

6503 

6548 

6593 

6637 

6682 

6727 

45 

970 

986772 

6817 

6861 

6906 

6951 

6996 

7040 

7085 

7130 

7175 

45 

971 

7219 

7264 

7309 

7353 

7398 

7443 

7488 

7532 

7577 

7622 

45 

972 

7666 

7711 

7756 

7800 

7845 

7890 

7934 

7979 

8024 

8068 

45 

973 

8113 

8157 

8202 

8247 

8291 

8336 

83S1 

8425 

8470 

8514 

45 

974 

8559 

8604 

8648 

8693 

8737 

8782 

8826 

8871 

8916 

8960 

45 

975 

9005 

9049 

9094 

9138 

9183 

9227 

9272 

9316 

9361 

9405 

45 

976 

9450 

9494 

9539 

9583 

9628 

9672 

9717 

9761 

9806 

9850 

44 

977 

9895 

9939 

9983 

**2S 

**72 

*117 

*161 

*206 

*250 

*294 

44 

978 

990339 

0383 

0428 

0472 

0516 

0561 

0605 

0650 

0694 

0738 

44 

979 

0783 

0827 

0871 

0916 

0960 

1004 

1049 

1093 

1137 

1182 

44 

980 

991226 

1270 

1315 

1359 

1403 

1448 

1492 

1536 

1580 

1625 

44 

981 

1669 

1713 

1758 

1802 

1846 

1890 

1935 

1979 

2023 

2067 

44 

982 

2111 

2156 

2200 

2244 

2288 

2333 

2377 

2421 

2465 

2509 

44 

983 

2554 

2598 

2642 

2686 

2730 

2774 

2819 

2863 

2907 

2951 

44 

984 

2995 

3039 

3083 

3127 

3172 

3216 

3260 

3304 

3348 

3392 

44 

985 

3436 

34SO 

3524 

3568 

3613 

3657 

3701 

3745 

3789 

3833 

44 

986 

3877 

3921 

3965 

4009 

4053 

4097 

4141 

4185 

4229 

4273 

44 

987 

4317 

4361 

4405 

4449 

4493 

4537 

4581 

4625 

4669 

4713 

44 

988 

4757 

4801 

4845 

4889 

4933 

4977 

5021 

5065 

5108 

5152 

44 

989 

5196 

5240 

5284 

5328 

5372 

5416 

5460 

5504 

5547 

5591 

44 

990 

995635 

5679 

5723 

5767 

5811 

5854 

5898 

5942 

5986 

6030 

44 

991 

6074 

6117 

6161 

6205 

6249 

6293 

6337 

6380 

6424 

6468 

44 

992 

6512 

6555 

6599 

6643 

6687 

6731 

6774 

6818 

6862 

6906 

44 

993 

6949 

6993 

7037 

7080 

7124 

7168 

7212 

7255 

7299 

7343 

44 

994 

7386 

7430 

7474 

7517 

7561 

7605 

7648 

7692 

7736 

7779 

44 

995 

7823 

7867 

7910 

7954 

7998 

8041 

8085 

8129 

8172 

8216 

44 

996 

8259 

8303 

8347 

8390 

8434 

8477 

8521 

8564 

8608 

8652 

44 

997 

8695 

8739 

8782 

8S26 

8869 

8913 

8956 

9000 

9043 

9087 

44 

998 

9131 

9174 

9218 

9261 

9305 

9348 

9392 

9435 

9479 

9522 

44 

999 

9565 

9609 

9652 

9696 

9739 

9783 

9826 

9870 

9913 

9957 

43 

N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

D. 

EXPLANATIONS  OF  THE  PRECEDING  TABLES 

TABLE  I 
THE  ATOMIC  WEIGHTS  OF  THE  ELEMENTS 

This  table  contains  the  most  recent  values  of  the  atomic  weights  of  the  ele- 
ments, based  upon  the  following  standards  :  oxygen  — 16.000,  silver  =  107.87. 

There  seems  to  be  little  doubt  now  that  the  atomic  weight  of  silver  is  at 
least  as  low  as  107.87,  and  for  that  reason  all  of  those  values  which  have 
been  determined  by  means  of  silver  are  recalculated  to  this  basis. 

The  writer  has  ventured  to  give  the  atomic  weights  of  a  few  elements  to 
three  places  of  decimals,  but  it  must  be  remembered  that  the  third  place  is 
obtained  by  averaging  a  large  number  of  analyses,  and,  with  two  exceptions, 
it  is  not  definitely  known.  However,  in  view  of  the  fact  that  such  excellent 
work  has  been  done  in  revising  the  weights  in  these  special  cases,  it  seems 
probable  that  the  values  as  recorded  approach  more  closely  the  true  values 
than  would  be  the  case  if  the  third  place  were  dropped. 

TABLES  II-IV 

These  tables  contain  the  molecular  weights  *  of  common  compounds,  mul- 
tiples of  the  atomic  weights  of  common  elements,  and  of  some  common 
compounds. 

They  are  useful  in  calculating  the  amounts  of  substances  which  are  chemically 
equivalent  to  given  amounts  of  other  substances.  A  few  examples  will  illus- 
trate some  of  their  uses  : 

(1)  Calculate  the  weight  of  hydrochloric  acid  which  is  exactly  equivalent 
to  1.5  grams  of  sodium  carbonate. 

Na2CO3  +  2  HC1  =  2  NaCl  +  CO2  +  H2O. 
mol.  wt.  Na2CO3  :  mol.  wt,  HC1  x  2  :  :  1.5  grains  Na2CO3  :  x  grams  HC1. 

"  mol.  wt.  HC1  x  2  x  1.5 

=  wt.  HC1  required. 

mol.  wt.  Na2CO3 

*  The  accuracy  of  a  molecular  \veight  is  largely  determined  by  the  least  accurate  of  the 
atomic  weights  which  make  it  up.  For  example,  it  is  useless  to  give  the  molecular  weight  of 
sulphuric  acid  to  more  than  two  places  of  decimals,  although  the  atomic  weight  of  hydrogen  is 
known  within  a  few  units  in  the  fourth  place  of  decimals,  and  oxygen  is  the  standard. 

65 


66  EXPLANATIONS  OF  THE  PKECEDING  TABLES 

log  second  multiple  of  the  mol.  wt.  HC1  (Table  IV)  =  1.862870 
log  1.5  (table  of  logarithms)  =  0.17(3091 

sum  =  2.038901 

log  mol.  wt.  Na2C03  (Table  III)  =  2.025265 

difference  =  0.013696 

The  number  of  which  0.013696  is  the  logarithm  is  1.03203,  which  is  the  weight  of  HC1 
required. 

(2)  What  weight  of  silver  must  be  dissolved  in  nitric  acid  and  added  to 
a  solution  containing  two  grams  of  barium  chloride  in  order  to  precipitate 
exactly  all  of  the  chlorine? 

BaCl2  +  2  AgN08  =  2  AgCl  +  Ba  (N03)2 . 
mol.  wt.  BaCl2  :  at.  wt.  Ag  x  2  :  :  2  grams  BaCl2  :  x  grams  Ag. 

at.  wt.  Ag  x  2  x  2 

=  wt.  Ag  required. 

mol.  wt.  BaCl2 

log  second  multiple  at.  wt.  Ag  (Table  II)  =  2.333930 
log  2  (table  of  logarithms)  =  0.301030 

sum  -  2.634960 

log  mol.  wt.  BaCl2  (Table  III)  =  2.318627 

difference  =  0.316333 

The  number  of  which  0.316333  is  the  logarithm  is  2.07172,  which  is  the  weight  of  silver 
required. 

(3)  The  atomic  weights  of  many  of  the  elements  are  most  readily  and 
accurately  determined  by  preparing  certain  of  their  halides  in  a  state  of 
great  purity,  and  then  in  a  weighed  sample  of  such  material  determining  the 
exact  weight  of  pure  silver  which  is  equivalent  to  the  halogen.    From  such 
data  the  atomic  weight  of  the  element  in  question  may  be  easily  calculated 
by  means  of  the  tables.    For  example,  let  us  take  a  special  case  which  will 
illustrate  the  method :   A  weighed  sample  of  phosphorus  tribromide  was 
treated  in  such  a  manner  that  the  exact  weight  of  silver  equivalent  to  the 
bromine  it  contained  was  determined,  and  the  weight  of  silver  bromide 
formed  was  also  determined.    The  atomic  weights  of  bromine  and  silver 
being  accurately  known,  we  have  only  to  calculate  from  the  data  the  molecu- 
lar weight  of  phosphorus  tribromide  and  subtract  from  it  three  times  the 
atomic  weight  of  bromine  in  order  to  obtain  the  atomic  weight  of  phosphorus. 
Therefore  we  make  the  following  proportion : 

wt.  Ag  :  wt.  PBr3  : :  at.  wt.  Ag  x  3  :  mol.  wt.  PBrg . 


EXPLANATIONS  OF  THE  PRECEDING  TABLES  67 

In  this  calculation  we  need,  in  addition  to  the  logarithms  of  the  first  two 
terms  of  the  proportion,  the  logarithm  of  the  third  multiple  of  the  atomic 
weight  of  silver,  and  the  third  multiple  of  the  atomic  weight  of  bromine, 
both  of  which  are  given  in  Table  II. 

To  calculate  the  same  value  from  the  weight  of  silver  bromide  formed, 
which  incidentally  serves  as  a  check  on  the  first  value  and  also  gives  one  a 
clear  idea  of  the  purity  of  the  precipitate,  we  make  the  following  proportion : 

wt.  AgBr  :  wt.  PBr3  : :  mol.  wt.  AgBr  x  3  :  mol.  wt.  PBr3 . 

The  third  multiple  of  the  molecular  weight  of  silver  bromide  is  given  in 
Table  IV. 

The  tables  are  also  useful  in  making  standard  solutions,  especially  those  of 
certain  normalities,  as  in  many  cases  it  is  only  necessary  to  shift  the  decimal 
point  in  the  proper  value  in  order  to  ascertain  the  weight  of  substance  which 
a  liter  of  the  standard  solution  should  contain. 

A  normal  solution  contains  in  a  liter  of  solution  a  gram  molecular  weight 
of  substance  reduced  to  a  univalent  basis. 

Two  examples  will  serve  to  indicate  the  method  of  using  the  tables  for 
this  purpose. 

NOTE.  It  is  scarcely  necessary  to  call  attention  to  the  rule  of  decimal  fractions,  i.e. 
that  to  divide  by  10  is  equivalent  to  moving  the  decimal  point  one  place  to  the  left  in 
the  dividend  ;  that  to  divide  by  100  is  equivalent  to  moving  the  point  two  places  to  the 
left,  etc. 

SOLUTIONS  OF  HYDROCHLORIC  ACID  OF  CERTAIN  NORMALITIES 

JV=mol.  wt.  (Table  III). 
N  _  mol.  wt.  __  mol.  wt.  x  5 
~2~~         2  10 

N      mol.  wt.       mol.  wt.  x  2 


55  10 

N  _  mol.  wt. 

To~     10 

N_  _  mol.  wt.  __  mol.  wt.  x  4 
25~       25  100 

N  _  mol.  wt.       mol.  wt.  x  2 
50  ~~       50  100 

N  _  mol.  wt. 
100~      100 


(Table  IV). 


(Table  III). 

(Table  IV). 

(Table  IV). 
(Table  III). 


68  EXPLANATIONS  OF  THE  PRECEDING  TABLES 

SOLUTIONS  OF  SODIUM  CARBONATE  OF  CERTAIN  NORMALITIES 
N  =  moLwt.  ^  mol.wt.x6 

N      mol.  wt.       mol.  wt.  /n 


N   mol.  wt.   mol.wt.  x  5  ,,T 

—  =  —    —  =0=  —    (Table  IV). 

10   2  x  10       100 

N   mol.  wt.   mol.  wt.  x  2  .„ 

2^  =  T^^--ToO--(TableIV)- 

N   mol.wt.  ^mol.wt 

50   2  x  50     100 
N_  =  mol.  wt.  ^  mol.  wt.  x  5 
100   2  x  100      1000 


TABLE  V 

REDUCTION  OF  COMPOUNDS  FOUND  TO  CONSTITUENTS 
SOUGHT  BY  MULTIPLICATION 

This  table  is  intended  to  aid  in  calculations  connected  with  the  analysis  of 
mineral  substances,  where  it  is  so  frequently  necessary  to  determine  a  given 
substance  in  a  state  of  combination  different  from  that  the  proportionate 
amount  of  which  we  wish  to  know.  If,  for  example,  we  wish  to  determine 
the  amount  of  barium  a  given  substance  contains,  we  should  probably  pre- 
cipitate it  and  weigh  it  as  barium  sulphate  and  from  this  weight  calculate 
the  barium  as  follows  : 

mol.  wt.  BaS04  :  at.  wt.  Ba  : :  wt.  BaSO4  :  wt.  Ba. 

at'Wt-Ba       xwt.BaSO<  =  wt.Ba. 
mol.  wt.  BaS04 

The  constituent  sought,  in  this  case  barium,  is  given  in  the  first  column  of  the 
table,  and  the  state  of  combination  in  which  it  is  convenient  to  determine 
the  substance,  barium  sulphate,  is  given  in  the  second  column.  On  the  same 
horizontal  line  with  BaS04  a  factor  is  given  which  is  the  quotient  resulting 
from  the  division  of  the  atomic  weight  of  barium  by  the  molecular  weight 
of  barium  sulphate,  so  that  it  is  only  necessary  to  add  to  the  logarithm  of 
this  factor  the  logarithm  of  the  actual  weight  of  barium  sulphate  in  order  to 
obtain  the  logarithm  of  the  required  weight  of  barium. 

From  the  above  it  is  plain  that  the  factors  express  the  actual  weight  of 
substance  sought,  contained  in,  or  equivalent  to  one  gram  of  substance  found ; 
that  is,  the  first  term  of  the  proportion  is  reduced  to  unity,  the  second  term 


EXPLANATIONS  OF  THE  PBECEDING  TABLES  69 

is  expressed  by  the  factor,  the  third  term  is  the  weight  of  substance  found. 
By  multiplying  the  second  and  third  terms  together  the  product  expresses 
the  weight  of  substance  sought. 

(2)  In  analyzing  orthoclase  feldspar  the  potassium  and  sodium  are  sepa- 
rated from  the  rest  of  the  constituents  and  weighed  together  as  chlorides. 
The  potassium  is  then  separated  from  the  sodium  in  the  usual  manner  and 
weighed  as  K.2PtCl6.  It  is  customary  to  express  the  results  of  such  analyses 
in  percentages  K20  and  Na.20.  From  the  weight  of  combined  chlorides  and 
the  weight  of  K.2PtCl6  the  weights  of  K20  and  Na20  are  calculated  as  follows  : 

mol.  wt.  K2PtCl6  :  chem.  equiv.  wt.  K2O  : :  wt.  K2PtCl6  :  wt.  K2O. 

\vt.  K2PtCl6  x  0.19383  (factor)  =  wt.  K2O. 
mol.  wt.  K2PtCl6  :  chem.  equiv.  wt.  KC1  (2  KC1)  : :  wt."K2PtC!6  :  wt.  KC1. 

wt.  K2PtCl6  x  0.30683  (factor)  =  wt.  KC1. 

wt.  of  combined  chlorides  —  wt.  KC1  =  wt.  NaCl. 

chem.  equiv.  wt.  NaCl  (2  NaCl)  :  mol.  wt.  Na2O  : :  wt.  NaCl  :  wt.  Na2O. 

wt.  NaCl  x  0.53028  (factor)  =  wt.  Na2O. 

CALCULATION  OF  INDIRECT  ANALYSIS 

Let  us  suppose  that  we  have  a  mixture  of  a  chloride  and  a  bromide,  and  that 
we  wish  to  determine  the  chlorine  and  the  bromine.  The  weight  of  silver  which 
is  equivalent  to  the  combined  halogens  is  determined  by  the  Volhard  method. 
Then  the  precipitated  AgCl  and  AgBr  are  collected  and  weighed  together. 

Let  x  -  wt.  AgCl, 

and  y  =  wt.  AgBr. 

Then  x  +  y  =  a  (wt.  of  AgCl  +  AgBr), 

and  — i-  x  -\ —  y  =  b  (wt.  Ag  equiv.  to  Cl  and  Br). 

AST  Ag 

As       ^    and       *    are  constant  quantities,  we  may  represent  them  by  k  and 

k'  respectively.    The  equations  then  become 

x  +  y  -  a, 
kx  +  k'y  =  b. 

Multiplying  the  first  equation  by  k  and  subtracting  the  second  from  it  in 
order  to  eliminate  a*,  we  have 

kx  +  ky  =  ka, 
kx  +  k'y  =  6, 
(k  -k'}y  =  ka-  6, 

ka-b 

y  =  - 77- 

k  —  k 


70  EXPLANATIONS  OF  THE  PRECEDING  TABLES 

As  k  —  k'  is  a  single  constant  we  have  y  =  —p  —   By  substituting  the  value 
thus  obtained  for  y  in  the  first  equation  we  have  x  =  a  —  value  of  y. 

wt.  AgCl  x  0.24737  =  wt.  Cl. 
wt.  AgBr  x  0.42555  =  wt.  Br. 

The  values  of  —  -  and  -     -  are  given  in  Table  V  under  Ag  and  opposite 
Agl>r          -A-gOi 


AgBr  and  AgCl  respectively. 

TABLES  VI-IX 

Normal  atmospheric  pressure  is  equal  to  the  pressure  exerted  at  sea  level 
and  45°  latitude  by  a  vertical  column  of  pure  mercury  760  mm.  long,  the 
temperature  of  which  is  zero  degrees  C. 

Barometric  readings  made  under  ordinary  conditions  must  be  reduced  to 
standard  conditions  ;  that  is,  corrections  must  be  applied  for  temperature, 
latitude,  and  elevation. 

Temperature  corrections.  In  view  of  the  fact  that  the  cubical  expansion  of 
mercury  is  much  greater  than  that  of  glass,  and  the  length  of  the  barometer 
scale  also  changes  with  the  temperature,  it  is  necessary  to  consider  all  of  these 
factors  in  making  the  temperature  corrections.  However,  these  have  been 
combined  and  the  values  are  given  in  Table  VI. 

Latitude  corrections.  Gravity  at  45°  latitude  and  sea  level  is  considered 
normal.  The  values  of  this  force  in  other  latitudes  as  compared  with  the 
normal,  taken  as  unity,  are  given  in  Table  VII  for  a  few  important  places. 
The  length  a  barometric  column  of  any  latitude  would  have  if  it  were  acted 
upon  by  normal  gravity  may  be  calculated  by  multiplying  the  observed 
reading  by  that  fraction  which  the  force  of  gravity  at  the  latitude  in  question 
is  of  normal  gravity,  or  the  proper  correction  may  be  taken  from  Table  VIII,  A. 

Elevation  corrections.  These  are  necessary,  because  gravity  diminishes  as 
we  proceed  from  the  center  of  gravity  of  the  earth  (Table  VIII,  B). 

Capillary  depression  corrections.  Manufacturers  of  straight  barometers 
make  due  allowance,  in  the  adjustment  of  the  scale,  for  capillary  depression 
of  the  mercury  ;  and  in  U-shaped  barometers  and  manometers  the  forces  on 
the  two  surfaces  compensate,  provided  the  mercury  is  of  uniform  purity  and 
the  arms  are  of  the  same  diameter.  However,  there  are  other  purposes  for 
which  the  values  of  the  capillary  depression  of  mercury  may  be  needed,  and 
they  are  given  in  Table  IX. 


EXPLANATIONS  OF  THE  PRECEDING  TABLES  71 

TABLES  XII  AND  XIII 

REDUCTION  OF  GAS  VOLUMES  TO  NORMAL  CONDITIONS  OF 
PRESSURE  AND  TEMPERATURE 

Boyle's  Law.  The  volume  of  a  given  mass  of  any  gas  varies  inversely  as  the 
pressure  upon  it,  provided  the  temperature  remains  constant. 

If  v  represents  the  volume  of  a  given  mass  of  gas  at  760  mm.  pressure, 
and  vl  any  other  volume  of  the  same  mass  at  the  pressure  h,  then  760  v  =  hv^ 


In  order  to  calculate  the  volume  any  given  amount  of  gas  would  have  if  it 
existed  under  normal  pressure,  we  have  only  to  add  to  the  logarithm  of  the 

observed  volume  the  logarithm  of  the  value  of  =™  '  taken  from  Table  XII. 

The  sum  will  be  the  logarithm  of  the  required  volume. 

Moist  gases  are  assisted  in  sustaining  the  pressure  of  the  atmosphere  by 
the  partial  pressure  of  water  vapor.  Therefore,  in  order  to  find  the  pressure 
which  the  gas  itself  is  actually  exerting  (which  is  equal  to  the  pressure  under 
which  it  exists  in  equilibrium),  we  must  subtract  from  the  pressure  of  the 
atmosphere  the  aqueous  tension. 

If  the  volume  of  a  gas  cannot  be  measured  under  exactly  atmospheric 
pressure,  it  is  frequently  convenient  to  determine  its  pressure  by  measuring 
the  difference  between  it  and  that  of  the  atmosphere  by  means  of  an  open 
arm  manometer.  The  pressure  of  the  atmosphere  is  then  altered  by  the 
amount  of  this  difference  in  order  to  ascertain  the  pressure  under  which  the 
gas  exists.  The  pressure  which  the  gas  alone  exerts  is  represented  by  h  of 
Table  XII. 

Charles's  Law.  The  volume  of  any  gas  increases  by  -^fa  part  of  its  vol- 
ume at  0°  C.  for  every  degree  its  temperature  increases. 

If  Vt  is  the  volume  of  a  gas  at  the  temperature  t,  we  have 

Vt  =  V0  +  F0  x  0.00367*  =  F0(l  +  0.00367*);  then  F0  - 


The  values  of  -  —  —  are  given  in  Table  XIII  for  temperatures 

1  -f-  U.UUoo*  t 

ranging  from  0°  to  149°. 

To  calculate  the  volume  a  given  amount  of  gas  would  have  if  its  tempera- 
ture were  reduced  to  zero,  we  have  to  add  to  the  logarithm  of  the  observed 


72  EXPLANATIONS  OF  THE  PRECEDING  TABLES 

volume  the  logarithm  of  the  value  of  Q0367  £   (Table  xni)>    The  sum 

will  be  the  logarithm  of  the  required  volume. 

We  may  combine  the  expressions  given  above  if  we  wish,  as  is  usually  the 
case,  to  reduce  the  volume  to  standard  conditions  of  both  pressure  and  tem- 
perature, thus 

FOP,  reomm.  =  4  x  1  + 0.00367  <  X  r'°'  *"""• 

These  reductions  may  be  summed  up  as  follows:  Correct  the  barometric 
reading  for  temperature,  latitude,  and  elevation.  Subtract  from  the  corrected 
reading  the  tension  of  aqueous  vapor,  and  apply  the  manometer  correction, 
if  there  be  one.  The  result  is  the  value  represented  by  h.  Add  to  the  loga- 
rithm of  the  observed  volume,  the  logarithm  of  ——  (Table  XII)  and  of 

j  i  \)\) 

T  A  AAQgrr  ^  (Table  XIII).  The  sum  will  be  the  logarithm  of  the  required 
J.  -f-  U.UUobi  t 

volume. 

TABLE  XIV 

This  table  is  intended  to  minimize  the  labor  of  reducing  the  volume  of 
moist  gases  to  normal  conditions  and  dry.  It  is  assumed  that  the  temperature 
of  the  barometer  and  of  the  gas  and  water  over  which  the  gas  is  measured  is 
the  same.  Under  this  condition  the  barometric  reading  is  corrected  for  tem- 
perature, the  tension  of  aqueous  vapor  subtracted,  and  the  resulting  value  of 

— —  combined  with AAQ/T-     ^or  certain  combinations  of  temperature 

4  oU  1  -j-  U.UUoo^  t 

and  pressure. 

Take  from  the  table  the  logarithm  corresponding  to  the  temperature  and 
approximate  pressure.  Interpolate  to  find  the  logarithm  corresponding  to  the 
exact  pressure,  and  add  to  it  the  logarithm  of  the  observed  volume  of  the 
gas.  The  sum  will  be  the  logarithm  of  the  volume  under  normal  conditions 
and  dry. 

TABLE  XV 

If  one  wishes  to  know  the  weight  of  an  observed  volume  of  gas,  as  in  the 
analysis  of  nitrogenous  organic  substances  by  the  Dumas  method,  the  volume 
should  be  reduced  to  standard  conditions,  and  then  to  the  logarithm  of  this 
volume  add  the  logarithm  of  the  weight  of  one  liter  of  the  gas,  taking  care 
to  express  the  volume  read  off  as  a  fraction  of  a  liter. 


EXPLANATIONS  OF  THE  PRECEDING  TABLES  73 

TABLE  XXVIII 
BUOYANCY  OF  AIR 

In  view  of  the  fact  that  the  buoyant  effect  of  the  atmosphere  changes 
considerably  and  often  rapidly,  it  is  necessary  in  work  where  great  accuracy  is 
required  to  reduce  the  apparent  weight  of  a  substance  to  a  vacuum  standard. 

If  d  is  the  weight  of  1  cc.  of  air  and  v  the  volume  of  the  object  weighed, 
the  true  weight  is  w  -\-  vd,  where  w  is  the  apparent  weight. 

If  the  specific  gravity  of  the  substance  is  known,  its  volume  is  calculated 
by  dividing  its  weight  by  the  specific  gravity.  The  error  introduced  by  us- 

ing the  apparent  weight  instead  of  the  true  weight  in  the  expression  v  =  —  - 

w  s 

is  negligible.    Therefore  the  true  weight  of  a  substance  is  w  -\  —  d. 

S 

If  we  wish  to  obtain  absolute  weighings,  the  same  kind  of  correction  must 
be  applied  to  the  weights.  For  brass  weights  (s  =  8.3)  the  correction  is 
0.000145  per  gram.  This  correction  is  negative  and  is  to  be  subtracted  from 
the  calculated  true  weight  of  the  substance. 

The  true,  absolute  weight,  then,  of  a  substance  weighed  in  air  with  brass 

weights  is  WQ  =  iv  (  1  +  "  -  0.000145  J  . 

The  values  of  d  (Table  XVI)  are  calculated  for  760  mm.  pressure.  In  work 
where  the  greatest  accuracy  possible  is  required,  the  value  of  d  must  be 

reduced  to  the  existing  condition  of  pressure  ;  namely,  d  x  ^TT- 

In  many  instances,  however,  it  is  sufficiently  accurate  to  consider  d  constant 
and  equal  to  0.0012  g.  at  room  temperature.  Under  this  condition  the  above 
expression  becomes 


=  w  (l  +  ^j     _  0.000145^  =  w  (1  +  c).     (See  Table  XXVIII.) 


THE  COMMON  SYSTEM  OF  LOGARITHMS 

This  system  of  logarithms  is  in  general  use  because  it  greatly  abridges  numer- 
ical computation,  and  with  due  care  arithmetical  errors  are  largely  eliminated. 

The  logarithm  of  a  number  is  the  exponent  of  the  power  to  which  it  is 
necessary  to  raise  a  fixed  number,  in  order  to  produce  the  first  number.* 

*  The  definition  is  based  upon  the  assumption  that  there  always  exists  a  real  number  x  which 
satisfies  the  equation  bx  =  a,  where  a  and  b  are  positive  numbers  and  b  is  greater  than  1. 


74  COMMON  LOGARITHM S 

The  base  of  the  common  system  is  10,  and  since 

10°  =  1  10-!  =  0.1 

101  =  10  10-2  =  0.01 

102  =  100  10-3  =  0.001 

103  =  1000  10-4  =  0.0001 

it  follows  from  the  definition  of  a  logarithm  that 

log  1  =  0  log  0.1  =  -  1 

log  10  =  1  log  0.01  =  -  2 

log  100  =  2  log  0.001  =  -  3 

log  1000  =  3  log  0.0001  =  —  4 

It  is  quite  evident  from  the  above  table  that  the  logarithms  of  all  numbers 
between  0  and  1  are  negative  and  that  the  logarithms  of  all  numbers  greater 
than  1  are  positive. 

NOTE.  A  negative  number  is  considered  as  having  no  logarithm. 

We  see  also  that  the  logarithm  of  any  number  between  1  and  10  is  greater 
than  0  and  less  than  1 ;  thus 

log  2. 71  =  0.432969. 

The  logarithm  of  any  number  greater  than  10  and  less  than  100  is  greater 
than  1  and  less  than  2 ;  thus 

log  26.  =  1.414973. 

It  is  plain  that  if  a  number  is  not  an  exact  power  of  10,  its  logarithm 
must  consist  at  least  in  part  of  a  decimal  fraction. 

It  is  true  that  such  logarithms  can  be  expressed  only  approximately,  but  if 
the  fractions  are  given  to  six  places,  they  are  sufficiently  accurate  for  even 
the  best  atomic  weight  work. 

The  integral  part  of  a  logarithm  is  called  the  characteristic,  and  the  deci- 
mal part  the  mantissa.  In  the  case  just  given  1  is  the  characteristic  and 
.414973  the  mantissa  of  the  log  26. 

To  find  the  characteristic  of  the  logarithm  of  a  number : 

(a)  When  the  number  is  greater  than  unity,  the  characteristic  of  its  log- 
arithm is  one  less  than  the  number  of  digits  to  the  left  of  the  decimal  point. 
Thus  the  characteristic  of  the  logarithm  of  46783.85  is  4. 

(b)  When  the  number  is  less  than  unity,  subtract  from  9  the  number  of 
ciphers  between  the  decimal  point  and  the  first  significant  figure,  writing 
—  10  after  the  mantissa.    Thus  the  characteristic  of  the  logarithm  of  0.00089 
is  6  with  -  10  written  after  the  mantissa :  log  0.00089  =  6.949390  -  10. 


COMMON  LOGAKITHMS  75 

Some  prefer  to  combine  the  two  parts  of  such  characteristics,  writing  the 
result  as  a  negative  characteristic,  in  which  case  it  is  one  greater  than  the 
number  of  zeros  preceding  the  first  significant  figure.  The  minus  sign  is 
written  above  the  characteristic  to  show  it  applies  only  to  it,  for  in  construct- 
ing logarithmic  tables  it  is  convenient  to  make  all  mantissas  positive  even  if 
the  logarithm  is  a  negative  number.  For  example,  log  1  =  —  0.602060 ;  but 
since  -  .602060  =  —  1.  +  .397940,  this  may  be  written  log  £  =  1.397940  or 
9.397940  —  10  with  a  positive  mantissa.  In  order  to  avoid  complications  it 
is  best  to  adhere  to  the  first  form  of  expression  mentioned  under  (b)  ;  that  is, 
when  a  logarithm  has  a  negative  characteristic  to  add  10  to  and  subtract  10 
from  it.  For  example,  instead  of  writing  the  logarithm  —  1.  +  .397940,  or 
1.397940,  we  should  write  +  10  -  1.  +  .397940  -  10  =  9.397940  -  10.  This 
is  convenient  when  we  wish  to  divide  a  logarithm  by  a  number.  Since  man- 
tissas are  always  positive,  it  would  not  be  correct  to  divide  1.397940  by  2,  as 
we  should  confuse  the  positive  and  negative  parts.  If  the  form  9.397940  —  10 
is  used,  the  confusion  is  avoided,  and  the  result  of  the  division  by  2  is 
4.698970  —  5  =  1.698970,  the  actual  logarithm  resulting  from  the  division. 


TABLE  OF  LOGARITHMS 

The  great  value  of  the  common  system  of  logarithms  for  the  purposes  of 
the  analytical  chemist  is  due  to  the  fact  that  short  tables  can  be  constructed 
which  contain  the  mantissas  of  the  logarithms  of  all  numbers  from  1  or  100 
to  some  given  number,  generally  1000  or  10,000,  this  being  sufficient  to  cover 
all  cases,  and  the  characteristics  can  be  determined  by  inspection. 

In  order  to  use  a  table  of  logarithms  one  must  know  how  to  find  the  loga- 
rithm of  any  number,  and  how  to  take  from  the  table  the  number  which  has 
a  given  logarithm,  and  also  how  to  point  the  numbers  off. 

To  find  from  the  table  the  logarithm  of  any  number : 

(a)  When  the  number  consists  of  two  significant  figures. 

All  of  these  numbers  are  given  on  the  first  page  of  the  table  in  columns 
marked  N.  The  logarithm  of  each  number  is  placed  opposite  the  number. 

(b)  When  the  number  consists  of  three  or  four  significant  figures. 

Find  in  the  column  of  numbers  the  first  three  significant  figures  of  the 
given  number,  then  glance  across  the  page  along  a  horizontal  line  to  the  col- 
umn under  the  fourth  figure  of  the  given  number  ;  four  figures  of  the  required 
mantissa  are  given  at  this  point,  to  which  two  figures  taken  from  the  zero 
column  must  be  prefixed.  If  the  four  figures  of  the  required  mantissa  are 


T6  COMMON  LOGARITHMS 

opposite  a  row  of  six  figures  in  the  zero  column,  the  first  two  of  the  six  are 
to  be  prefixed  ;  but  if  they  are  opposite  only  four  figures  in  the  zero  column, 
the  two  figures  to  be  prefixed  will  be  found  above,  unless  in  passing  back  to 
the  zero  column  asterisks  be  met  with,  in  which  case  the  two  figures  will  be 
found  immediately  below  the  horizontal  line  in  the  zero  column.  Zeros 
should  be  written  wherever  asterisks  occur.  Characteristics  are  then  prefixed 
in  accordance  with  the  rules  already  given. 

Examples  :  log  106  =  2.025306 
log  1264  =  3.101747 
log  2041  =  3.309843 
log  2042  =  3.310056 
log  2048  =  3.311330 

(c)  When  the  number  consists  of  more  than  four  significant  figures. 

The  mantissas  of  the  logarithms  of  these  numbers  are  not  to  be  found  in 
the  table,  but  they  can  be  easily  calcuMted  from  values  given  in  the  table 
by  a  process  of  interpolation.  The  principle  of  proportional  parts  assumes 
that  for  a  small  change  in  a  number  there  corresponds  a  proportional  change 
in  the  logarithm.  This  is  not  strictly  true,  but  the  approximation  is  suffi- 
ciently close  for  most  purposes. 

For  example,  required  the  log  521257.  We  find  from  the  table  log  5212  = 
3.717004  and  log  5213  =  3.717088.  That  is,  an  increase  of  one  unit  in  the 
fourth  figure  produces  an  increase  of  .000084  in  the  logarithm.  Therefore 
an  increase  of  .57  of  this  unit  will  produce  an  increase  in  the  logarithm 
equal  to  .57  x  .000084,  or  .000048.  Hence  log  521257  =  5.717052. 

NOTE.  In  order  to  facilitate  the  process  of  interpolation  it  is  customary  to  give  the 
differences  between  the  logarithms  of  consecutive  numbers  of  four  figures  in  a  separate 
column.  Such  numbers  are  called  tabular  differences.  In  the  table  one  number  is  given  at 
the  end  of  each  horizontal  line,  and  in  each  case  it  is  nearly  a  mean  of  the  differences 
of  any  two  logarithms  on  the  same  line.  It  is  intended  that  these  numbers  should 
serve  only  as  a  guide,  and  the  last  figure  should  be  checked  in  every  instance  by  glancing 
at  the  logarithms  involved. 

The  following  rule  is  derived  from  the  above  :  Place  a  decimal  point  after 
the  fourth  significant  figure  from  the  left,  converting  the  given  number  into 
a  whole  number  and  a  fraction,  and  this  irrespective  of  any  decimal  point 
that  may  occur  in  the  given  number.*  Find  from  the  table  the  mantissa 

*  Numbers  with  the  same  sequence  of  figures  and  which  differ  only  in  the  position  of  the 
decimal  point  have  the  same  mantissa,  for  one  is  the  product  of  the  other  and  an  integral  power 
of  10 ;  hence  their  logarithms  differ  only  by  integers.  Therefore  the  mantissa  of  the  common 
logarithm  of  a  number  is  independent  of  the  decimal  point. 


COMMOX  LOGARITHMS  11 

of  the  entire  part  and  multiply  the  decimal  part  by  the  tabular  difference ; 
add  the  product  thus  obtained  to  the  mantissa  of  the  entire  part  and  prefix 
the  proper  characteristic,  determined  with  respect  to  the  position  of  decimal 
point  in  the  original  number. 

To  find  from  the  table  the  number  which  corresponds  to  a  given  logarithm  : 

(a)  Required  the  number  the  logarithm  of  which  is  1.874772.  We  find  this 
exact  mantissa  given  in  the  table,  and  opposite  in  the  column  of  numbers  we 
find  749,  the  first  three  figures  of  the  required  number,  and  at  the  head  of 
the  column  5  the  fourth  figure. 

(&)  Required  the  number  the  logarithm  of  which  is  2.137860.  The  man- 
tissa of  this  logarithm  is  not  given  in  the  table,  but  it  lies  between  the  two 
mantissas  .137671  and  .137987,  and  the  numbers  corresponding  to  these  are 
1373  and  1374  respectively.  The  difference  between  the  two  mantissas 
taken  from  the  table  is  316,  and  the  difference  between  the  given  mantissa 
and  the  smaller  of  the  two  taken  from  the  table  is  189 ;  that  is,  an  increase 
of  316  in  the  mantissa  produces  an  increase  of  one  unit  in  the  corresponding 
number.  Therefore  an  increase  of  189  in  the  smaller  of  the  two  mantissas 
taken  from  the  table  will  produce  an  increase  of  ^ff  of  a  unit  in  the  cor- 
responding number.  Hence  the  required  number  is  137.359  nearly. 

The  following  rule  is  derived  from  the  above : 

Search  in  the  table  for  the  mantissa  of  the  given  logarithm,  and  if  it  cannot 
be  found,  set  aside  the  number  corresponding  to  the  next  less  mantissa.  Sub- 
tract this  mantissa  from  that  of  the  given  logarithm  and  divide  the  remainder 
by  the  tabular  difference,  carrying  the  division  as  far  as  desirable.  Annex  the 
quotient  to  the  number  set  aside,  and  point  off  from  the  left  one  more  integer 
figure  than  there  are  units  in  the  characteristic  of  the  given  logarithm.  If 
the  characteristic  is  negative,  the  number  is  less  than  1,  and  the  number  of 
zeros  to  be  placed  before  the  first  figure  is  one  less  than  the  number  of  units 
in  the  characteristic. 

MULTIPLICATION  BY  LOGARITHMS 

Find  from  the  table  the  logarithms  of  all  the  numbers  to  be  multiplied 
together.  Add  these  algebraically,  remembering  that  negative  signs  apply 
only  to  the  characteristic.  The  sum  is  the  logarithm  of  the  product. 

Thus  multiply  27.1  by  119.86. 

log  27.1    =  1.432969 
log  119.86  =  2.078674 

3.511643  =  log  of  product 

The  number  of  which  this  is  the  logarithm  is  3248.201. 


78  EXPLANATIONS  OF  THE  PEECEDING  TABLES 

DIVISION  BY  LOGARITHMS 

Find  the  logarithm  of  the  dividend  and  subtract  from  it  the  logarithm  of  the 
divisor.  The  difference  is  the  logarithm  of  the  quotient.  The  word  "  differ- 
ence "  is  used  here  in  its  algebraic  sense.  That  is,  if  the  characteristic  of  the 
logarithm  of  the  divisor  is  negative,  its  sign  must  be  changed ;  but  if  that  of 
the  dividend  is  negative,  it  must  be  treated  as  a  negative  quantity.  Let  it  be 
said  once  more  that  mantissas  without  exception  are  positive. 

1.  To  divide  100.07  by  56.07. 

log  100.07  =  2.000304 
log  56.07  =  1.748731 

0.251573  =  log  of  quotient 

The  number  of  which  this  is  the  logarithm  is  1.78473. 

2.  To  divide  107.87  by  0.0187779. 

log  107.87  =  2.032901 
log  0.0187779  =  2.273647 

3.759254  =  log  of  quotient 

The  number  of  which  this  is  the  logarithm  is  5744.5. 

3.  To  divide  0.13736  by  153.36. 

log  0.13736  =  1.137860 
log  153.36  =  2.185712 

4.952148  =  log  of  quotient 

The  number  of  which  this  is  the  logarithm  is  .00089568. 

In  regard  to  involution  and  evolution  it  is  only  necessary  to  say  that  the 
logarithm  of  any  power  of  a  number  is  obtained  by  multiplying  the  loga- 
rithm of  the  number  by  the  exponent  of  the  power,  and  that  the  logarithm 
of  any  root  of  a  number  is  obtained  by  dividing  the  logarithm  of  the  number 
by  the  index  of  the  root. 


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